Are we not gonna cry? Because I am. I am gonna cry. Like, I am everything I've ever wanted. Fun welcome back to my channel. I hope you're all good. Today I have been so excited for this video. We're doing a book haul today. I think this is one of my biggest book hauls ever and I also think it's one of my most beautiful book hauls ever. We have hauled some of my favourite covers I think I've ever hauled. So it's a momentous moment and today the future starts. I feel like today the future starts. So it's a good day. So first, these are the books I'm most excited for. These four books. I listen. Some of you may know I have an obsession with the cover of my edition of The Mystery of the Blue Train by Agatha Christie and let me tell you I learned. It's getting weird. I learned that that is a like collection that Harper Collins had done of some of Agatha Christie's most famous books and then one day I got an email from Harper Collins saying that on their site of their books they had 40% off and I was like Megan it's now or never. Megan you may have no money but it is now or never. You will regret this for the rest of your life if you don't do it. So I bought most of the ones in the collection that I don't have. Are you ready?   So we have got I don't think you're ready. Look how beautiful. We have got Murder on the Orient Express which is gorgeous. Then we have got Death on the Nile. Then we hold it like that so you can really see it. I'll do close-ups as well.  Because I think you are. Then we've got the ABC Murders. I love the kind of like geometric design on this one and then we've got I also love this one the 450 from Paddington right?  So I got these four editions and let me just tell you they are just this isn't doing them justice how gorgeous they are. I have never seen more gorgeous books in my life. I adore them. I love them so much. I would die for them. I don't know what my favorite one is out of these. Maybe the ABC Murders. Here's the thing. I think my favorite changes every day. I'm fickle. So right now I think it's that one but if you ask me tomorrow it's going to be Death on the Nile. So I just love these as many of you know I am reading all the Urquiporo books in order at the moment. These three are Urquiporo right? Or am I making it up? And then this is Miss Marpo I think. I just love these. These are like prized possessions. I'm tempted to put them on my bookshelf soon and just have them displayed there even though I haven't read them because they they are literally that beautiful and I love them so so much. They are literally some of my favorite books I have ever bought. Then along with those books I also bought Black Out by um Donnel Clayton, Nick Stone, Tiffany D Jackson, Ashley Woodfolk, Angie Thomas, and Nicola Yoon. So these authors all come together and written this book and it's about a blackout in New York City and about these different like love stories that happen during that blackout. A lot of them are linked. I have listened to a few like interviews and podcasts that they've done talking about this like in the promo for it. There's a lot of like links between the stories so I am so excited to get to this. I'm thinking maybe this is going to be a holiday read? I'm not sure. I don't know how much I'm going to read on holiday. Am I going to read loads? Am I going to read like five books? I'm not going to read at all. Next let's show you this one quickly. This is one of my favorite covers of the year of any 2021 new release. Again you're going to cry. That is my reaction to covers that I love. I just like I just want to cry. I just want to cry. Just like leave me alone in a dark room to cry. Very strange. This was very kindly gifted to me by a subscriber called Trinity. So thank you so much Trinity and it is are we ready? Moment of silence. Okay it is the ones we're meant to find by Joan Key. So this is a sci-fi about these two sisters and one of them lives in this like super futuristicy town and the other one I think has been like deserted on an island and they're trying to find their way back together. I have heard mixed things about this since it's come out. I think everyone's in agreement that it's like the most beautiful cover but I have heard mixed things on the on the content. I've heard some good things. I've heard some not so good things. I've heard it's like quite complicated sci-fi and listen we all know one brain cell. One I can't even say cell. I said sales. Not even one brain cell. I am a bit nervous to read it but I'm also so excited because it is a beautiful cover. It's a shame I didn't have this when I did my most beautiful covers. Do they equal beautiful books? Because this would have been on the list but it is gorgeous. I mean my conclusions in that video if you haven't watched it. Beautiful covers don't mean beautiful insides of books but I'm hoping this will break the mold and I will love it. So next are some books that my parents very kindly bought for me as like a present for getting a first at uni. If you don't know I got my results back from my university degree which I just finished and I got off that. Let's just get into it because are you ready for another beautiful book? Are you ready? This is why I'm telling you there are so many beautiful books in this haul. We're gonna cry again. I'm gonna cry again. Okay. Oh my god. Jesus Christ. Check out the label. This is the Tea Dragon Tapestry by Kay O'Neill. This is the third in the Tea Dragon series but the second was a prequel and I say it again. I cannot find it anywhere. I mean look at how gorgeous the insides are. Again I will do close-ups but like aren't you crying? I am crying about these Tea Dragons who like brew tea and it's just so cute and wholesome and soft and I just love it. So I am so happy to finally own this. It is genuinely just the most beautiful lovely illustration stories. It's like a warm hug as a book and I am so excited to continue on with the series. Like it's just stunning. It is I think the prettiest graphic novels I've ever read. I just absolutely love them. It's like a warm hug. It's like a warm tea. It's like a warm chamomile tea. If this was a book I would just hug it non-stop. It reminds me of like a teddy bear. It is the personification bookification for teddy bear.  I tell you now. Oh this is a beautiful cover as well. I chose A Lapse Away by Darcy Little Badger.  That was enough reason for me. I know this is about like an indigenous girl who I think can raise the spirits of the dead or is it dead animals? One of the two. And it's kind of like a middle grade but kind of not. I've just heard that this is like beautiful writing. Very atmospheric. Everyone who read this it was kind of like in their best books of the year last year. So another one I'm very very excited to get to hopefully soon. I don't have plans but hopefully I will get to that soon. Then what else did we pick? Well I picked these not we. Actually let's talk about the one of these that isn't a new release and then we'll talk about the three that are new releases. Technically the T-Dragon tapestries are new release as well. It is The Jeweled Moth by Catherine Wood Fine. This is the second in the Sinclair's Mysteries. I've spoken a little bit lately about how I made a series spreadsheet of every series I have started and it gave me a kick up the ass.  To finally carry on with some series and maybe like I don't think I'm gonna vlog reading this. I think this will just be a book that I read in my own time because sometimes I get caught up with like I can't read a book if I'm not vlogging it because I don't want you guys to like miss out on my thoughts or anything but it's also not true. Like this is a second book in a middle grade mystery series that I don't think you necessarily want a dedicated vlog for and like that space in a vlog would probably be better spent by putting a different book in there. Not to say like oh I can't put series in vlogs if I if I want to but I just feel like sometimes something like this would be good for me to just read on my own. So this is a middle grade murder mystery series set in like I think the 1900s. The first one was set at this department store called Sinclair's which is very much like Harrod's and our girls were working there and they came together to solve this mystery and it's just fun like I really like it. It presents itself as very campy like it's very like over-the-top dramatic fun. Wow! Woo! And then I picked three more new releases. First we have got the final girl support group by Grady Hendricks. I have always wanted to read some Grady Hendricks and I never have. He also wrote Horror Store which is the one that like looks like an IKEA catalog and my best friend's Exorcism so I've heard so many good things about so many of his books but this one is his latest release and it is about the support group of final girls of serial killers. So these women who have survived these like horrific things and they come together in the support group and I think they start getting killed off basically. I've heard some good things since this came out. It only came out like a couple weeks ago I think. I wanted to read more horror. Horror and sci-fi I think are genres I always really enjoy when I read them but I don't pick up enough so they're currently genres that I am like prioritizing hopefully reading a bit more from. Sure Jan. The next one oh my gosh I am so excited. This is another potential holiday holiday book. Can you tell I'm like I'm trying so hard to figure out what I'm gonna read on holiday and it's really it's really hard. It's really it's a really hard decision but I got Switch by AS King. Oh my gosh I'm so excited. Me and AS King have a have an interesting relationship. I either give her books five stars or like two stars. I'm hoping this will be another five star. My hair is annoying me today. What is this strand of hair doing? Where has this strand of hair come from and why doesn't it want to amalgamate with the rest of my face? Like like why we keep gapping? Like you excuse me what is happening with this hair? I have never in my life the order to go like this. I was rooting for you. We were all rooting for you. I'll dare you.  It's told in these really short verse so we have like a chapter but within that chapter we have like little sections that have subheadings. AS King if you want wacky books just go to her like she's there for you. She's there with open arms.  I was angry. I was angry. I don't usually read like descriptions to you because it's kind of boring. No shade. No tino shade. But this one isn't. Time has stopped. It's been June 23rd 2020 for nearly a year as far as anyone can tell. Frantic adults demand a teenager's focus on finding practical solutions to the worldwide crisis. Not everyone is on board though. Javling Throne prodigy Truda Becker is pretty sure her solution time class wouldn't solve the world's problems but she does have a few ideas which might. Truda lives in a house with a switch that no one ever touches. A switch her father protects every day by nailing it into hundreds of progressively larger boxes but Truda's got a crowbar and one way or another she's going to see what happens when she flips the switch. So we're dealing with like bonkers level territory here. I am so excited. I think she like lives in one of the boxes. I don't know but I'm very very very excited for this and it's really short so I have no excuse for not reading it yet. Well I only got it like a couple days ago so actually I do have an excuse. But I did tell a bit of a lie there. And then finally of the books they got me. Another one that I am so dupe dupe dupe dupe dupe dupe excited for. This book haul like No Lie is like one of the best book hauls I've ever done in my life. We have Dead Dead Girls by Nikesa Afia. This is a mystery, a murder mystery set in Harlem 1926 where this black girl is the detective and it's going to be amazing. I've picked this up particularly from Mara from Books Like Woe's recommendation. I go to her for a lot of my mystery recommendations and I've heard that it's like quite a bit heavier than you would expect. I think looking at it Mara said this as well like looking at it you kind of expect cosy mystery vibes like it's that you know it's got that kind of like cosy historical vibes but I've heard it's a lot heavier. I think young black women are going missing and so this girl takes it upon herself to investigate it. So this is a mystery I'm really really excited for and I haven't heard a lot of people other than Mara speak about so I'm very much looking forward to it. Fairly books are always gorgeous. This one I have spoken about already so just very quickly we've got Fire with Fire by Desi Saria. This is a fantasy about twin sisters I think or no they're twins. I think they're just sisters.  I don't really know. I needed to do a video testing. Book box books it. Book box books. Book box books that I didn't know anything about beforehand because I need to test how you know how accurate I swear to God I swear I do not deserve this. I need to test how good they are but I don't really know anything about it so we're just gonna park it let me know if you've read it and if you think I'd like it. Now I have got the July July Fairly box. I haven't unboxed it yet so let's just do that quickly together. I am so excited. I think I know what this book may be and if it if I'm right I am so excited. Like this is a book that I am genuinely very very excited for. Oh we've got a tin. I love a book tin.  I pulled the lid off to find another lid. Um that does make no sense.  How do I open you? Does it not have an inside? It does okay we're good. So gorgeous book tin. Inspired by a quart of thorns and roses it's blue it says be glad of your human hearts pity those who don't feel anything at all.  What do we have here? Oh it is oh it is it is a book sleeve. Fairly do the best book sleeves because they have a zip. Before we even get into the design oh and this one is like fabric key on the inside. Oh that is that is oh that is bougie. They are bougie today.  I'm like why please all books need to have zips in my opinion. Anyway oh yeah they said we've improved it even further by using the same material we used in our pencil cases. That is so correct. That is that is correct. That is correct. Um that is correct. Very nice quality. This is gorgeous. This is inspired by the blood of star astrology by Elizabeth Lim. That is so pretty I love the colors on it.  Fairly don't understand how much I love them. Like oh we've got an umbrella. Okay I'm not going to open this but it's got like cards on it and it's inspired by Heartless by Marissa Mayer which I have read and I did enjoy it. Yes I love socks. We've got these lovely sockies. Oh they're big socks. Inspired by Cinderella is dead which I have not read but I do own so here's hoping that I'm gonna love that and then we've got a foil print for the Star Dutch Queen series by Roshani Chopsky and we have got the tarot cards which are inspired by Carrival by Stephanie Garber. Okay let's have a look at the book. I'm hoping it is a certain book so let's see. Oh my gosh look at the sprayed edges already. I love it. I love it and it gives me that buzz. It feeds exactly what I want to do.  So this is Six Crimson Cranes by Elizabeth Lim. I have been so excited for this book. This is a 2020 release I've actually been super duper excited for. Are we crying? Yes we are. Look at the gorgeous stenciling of the cranes down the spine and then we've got purple on the other ends. Oh my god let me guess. Let me guess. No no I actually can't take it. I actually can't take it. I can't take it. Look at that. Can you see? Oh my oh my god on the spine. This is actually one of the most beautiful books I own. This is actually one of the most beautiful books I own. Do I read this on holiday? Listen watch me watch me watch me take about 20 books with me. I am so tempted right now. I think I'm gonna take this with me. Look at the gorgeous stenciling on the hardcover and then we've also got a gorgeous art on the back of the dust jacket. Fairly I want to marry you. I will leave them linked down below. Go check Fairly out if you haven't before. I just am a massive fan of them. Thank you so much to Fairly for sending this to me. I appreciate it so so much. I actually I actually am almost crying. Like this this book everything about this all the things they've added are so gorgeous. I actually feel a bit like blown away. Listen you guys can you get over it? It helps that pink is my favorite color but like guys yeah I love it. I love good news love good news I just love good news. Oh shit I forgot one of the books that my parents got for me it was not with the other ones. It's because my mom has just started reading this so I had to go grab it. I spoke about this in my TBR video. They got me Hairpin Bridge by Taylor Adams. This is by the author of No Exit which I love one of my favorite thrillers. It's about this girl whose sister supposedly killed herself by driving off this fridge and leaving a vague suicide note. She doesn't believe her sister killed herself she believed she was murdered and so it's about her going back to this place and the guy like the patrol um highway patrol guy being very evasive and so I think he's suspicious. Don't be suspicious you are suspicious. Don't let the killer get you. Like Halloween I think it's for ghouls and goblins and for the killer in disguise to choke you out.  I've got another fairy loop book to show you because it's been a couple months. We have got Witches Steeped in Gold by Sienna and Smart. Look how gorgeous this edition is. This is like this African inspired fantasy. I've heard so many good things about it. Literally everyone who again who reads this loves it and I love this redesign with the pattern on the dust jacket. Listen again like I said fairy loop doesn't know how to lose they just win. Then one of the first book I actually hauled I think this was the first book I hauled so ages ago but it is We Are Okay by Nina Lacour. If you watch my channel you know that I absolutely loved um oh my god why have I forgotten the name? Why have I forgotten the name?  Watch over me my Nina Lacour that's like one of the better books I think I've read this year. So this is another Nina Lacour. I don't know anything about this. I don't really know anything about the story but I am so excited to read it and I'm gonna be reading it this month for a secret video so stay tuned. I am so random I kind of about just did that. Next these are some of the books I am most excited for. I don't know why I've left them so late but let's be honest nothing but hits right? Nothing but hits nothing but wins. So these are some of the books I am most excited for. I bought two of these when I popped into Waterstones a couple weeks back and I could not contain myself. I really could not. I tried. I tried and I failed. I can't. I can't. I've tried it and I failed. Why does everyone excited then? So firstly I showed this in my TBR game as well. I got Ace of Spades by Farida and BK Eamede. This is a private school. It's gossip gun inspired. Our two main characters have secrets starting to be leaked out about them and when I put this in my TBR I uploaded it last night when I'm filming this. All of you were commenting how much you loved it, how amazing it was, how much you think I'm going to love it and I'm not ready.  I am not ready but I am so excited. I am so so excited. Then we have also got The Appeal by Janice Hallett. Now this was sold to me in Waterstones. This is why I bought these books because the woman there working there sold this to me.  It is a motor mystery set in a quaint English town. Breathe with me. Okay breathe with me. I'm not going to coin it. It is told to mixed media like emails and texts and all of that thing. It's entirely told through like emails. What? Excuse me? Are we not gonna cry? Because I am. I am gonna cry. Like I am everything I've ever wanted. I am so so excited to read this. I literally can't wait. It's going to be amazing. That's all I need to know. These two law students have been assigned to the case. Someone has already been sent to prison for murder but the person charged with the case believes they are innocent. So we're just going to go through all the evidence and like figure it out together. I want to cry. It's everything I have ever wanted. It's everything I've ever wanted. And then lord I got sent a proof of the Christie affair. This isn't the final cover. This is like the proof cover. But can we talk about what a cool proof cover this is? I must stand. Not gonna lie. I must stand. No I don't think you understand. I'm upset. So this is about when Agatha Christie went missing for about 11 days and this is told from the perspective of her husband's mistress which is kind of theorized to be the reason why Agatha Christie went missing.  She had some kind of mental break and she actually like signed into the hotel where she went and stayed in, I think it's either the mistress's name or the mistress's last name. One of the two. And so it's told from the mistress's perspective and I am already obsessed. You guys know me. You know I love Agatha Christie. You know I love murder mysteries. You love mysteries. This book has been written for me. Can you believe nothing but hits? Like I don't think I've ever had a book called like this. So yeah I am so excited to read this. It comes out in January 2022. So I've got a little while. I feel like this could be a good Christmas read. The lovely people over at Verso Books contacted me and wondered if I wanted to see a few of their books which I was super interested in because they are like a pretty well known more like left-wing publisher of non-fiction. I've always add up their books so I'm super excited to receive these and hopefully I'll read some of them soon. Firstly we have crippled austerity and the demonization of disabled people by Francis Ryan. So this is about how austerity in the UK has made disabled people be viewed as worthless, be viewed as scroungers and has kind of demonized the public perception of them. Which is a topic I'm very interested in. I don't think disability is talked about enough particularly in non-fiction. I've always said I wanted to read more non-fiction about disability. So this is now my chance. I'm very intrigued about this. Then we've got this tiny book called Feminism for the 99% and Manifesto. So I believe this is viewing feminism through the lens of anti-capitalism, eco-socialism and anti-racism. So it's kind of making sure your feminism is inclusive of all people and especially of the people who need it. So again I'm very excited for this. I feel like this would be maybe a good one for me to again not read in a vlog but just read on my own at some point. Then we have got Black Women's Lives in Britain. So this is reclaiming and recording Black Women's history throughout Britain. I'm sorry it's called Heart of the Race Black Women's Lives in Britain. Yeah like rewriting this history and making people aware of the history that Black women have in Britain which has so often been erased and ignored. So I think this is a super important topic as well. And then this is fiction actually. I don't think this is non-fiction but this is Terminal Boredom which is a collection I think of like seven short stories which have been translated from Japanese. I believe it's kind of like science fiction-y, speculative-y. Which you guys know I really enjoy. I love speculative fiction so I'm very excited to get to this as well. So thank you Verso Books for sending these for my way. I'm super excited to get to order them. And then I don't want to end this on a bum note. This is what I'm going to do. I'll be sitting on the floor. The last three books I will just hold up very quickly. They've been in a video and a wrap up but I did haul in the last couple months. Only Love Is Real by Dr Brian Weiss. The Four Agreements by Don Miguel Ruiz and Pretty Little Liars by Sarah Shepherd. These were all for the Reading Kylie Jenner's favourite books video which I will leave linked. It was interesting but I'm glad it's behind me. I'm glad there's in my past. So I'm not going to attempt and even hold up all these books but this is generally one of my favourite books because I've ever done. I think this is like nothing but hits like I say. Nothing but hits. Just like so many beautiful books. Let me know which like book here is your favourite to look at out of all the ones I showed. If you've gotten to the end comment um is there like card emojis? I think there must be. Comment anything related to playing cards basically. Anything along those vibes if you've gotten to the end. Thank you so much for watching. I will see you very soon in another video. Bye!


So, turning your workbooks to where there's a blank page at the very, very back. It's got a bunch of blank pages at the very, very back. Find a page that looks kind of nice and has a little heading here. You can write how to use GCs, how to use GCs, the graphing calculators, okay? The basics, that's the on button, okay?  Second function on is the off button. Yours will turn off after, I think, eight minutes of inactivity automatically to save the battery. By the way, if yours is saying low battery, ignore that for as long as you can. You can usually go for about two months with that low battery symbol before replacing them. If you need to replace them, it's four triple A's, get them from your drugstore, get them from shoppers drug, wherever, nearest whatever store. So first thing you want to do is clear your screen, clear, clear, clear. If you're stuck in a menu somewhere and you can't get out, clear, clear, clear, or second function quit, which is second function mode, that bails you out of almost everything. So before you freak out, do that, okay? Let's do a mathematical operation together. I want to type in eight to the fifth minus 100 times negative three. How do I type that in? Well, I type eight. Where's the exponent button here? Exponent button is right above the divided by the little hat symbol thingy there. Here's your, to the power of five minus 100 bracket. Now the most common mistake, and I want you all to look up because I said this in my last class and sure enough three kids did it even though I said it, there is a huge difference on these calculators between your negative symbol, which is right here, and the subtraction symbol, which is right here.  I'm going to pretend to make an error. I'm going to put a subtraction three. And if I hit enter, my calculator gives me an error, a syntax error. If you ever get this message, first of all, don't freak out means you type something wonky, but don't hit clear. One of the things I like about these calculators is if you pick option two, if I hit the number two, go to the error. It puts the cursor right where the glitch occurred. My cursor is flashing on that, it's like, I don't know what you mean there. That should be a negative. Look up, that's a negative, that's a subtraction. You can kind of see the difference, so a negative looks much smaller. Anyways, when you do that, you should get 33,068, yes? Let's take the square root of that. Here's your x squared button. The square root button is second function x squared. You'll notice as soon as you type a square root, it does an open bracket automatically, Holly. Did you see where the square root, by the way, I need you kind of with me here, second function x squared, it's a follow along, right there. I don't want to retype 33,068. Where's the answer button on my graphing calculator? Trevor, the answer button is second function negative, right above here you can see ants in yellow, anything in yellow is hit the yellow button. Close bracket, square root of it is<PHONE_NUMBER>, blah, blah, blah, blah, that's where the square root is. Brackets are here, what other stuff might you want? How do I find the sixth root of 5,430? I type 6, the math button right here, if you hit the math button, this has all your obscure mathematical functions, so if you press the math button, I can see option 3 is to cube, although I probably just go to the power of 3. Option 4 is cube root, option 5 is nth root, your generic root button. If I press option 5, and now I type 5,430, that will take the sixth root of that, and with that little x up there it's saying, look this number is really supposed to be there, but the graphics can't show that. The sixth root of 5,430 is 4.19264, blah, blah, blah, in fact, if I go 4.192438 to the power of 6, that should be really, really close to 5,430. So you okay where that is? 3 over 5 plus 7 over 8, how do I do fractions here? I literally go, don't worry about a common denominator, don't waste your time, that's math 8, I kind of like to assume that you know how to do it, but I'm also recognizing that I'm pressed for time, 3 slash 5 divided by 5 plus 7 divided by 8, enter. I should do it, that's a decimal, I want a fraction answer, no problem. One of the ones you'll use the most, especially in the probability section where we want our answers as fractions, if you press the math button again, the very first option goes from decimal to fraction, and so the really quick way to do that is to go hit the math button and then just go enter, enter, look what you have on your screen now, there it is, yes, enter, enter, 59 over 40, if I want to go 2 thirds plus 7 over 12, math, enter, enter, 5 over 4, nice and quick, type with me, 8 times 9 to the power of 3 minus 15, enter, it does the bed mass properly for you, 8 times 9 to the power of 3 minus 15, enter, you got 5, 8, 1, 7, don't, I made a mistake, I didn't want to put 8 times, I wanted to put 7 times, to bring back any line previous, if you go second function, enter, sorry, second function, enter, that brings back your last line of typing, and now I can go back, back, back, back, I said I wanted to change the 8 to a 7, I can delete the 7 with the delete button right here, don't, second function insert, which is shift delete, put a 7 there, as a matter of fact, if you go second function, enter, second function, keep hitting second function, enter, it remembers the last 20 lines I believe that you've typed, so if you just brought a calculator from me, it's like you're getting secret messages from whoever used this last year, you can see what their last equations were, some of those might be from the final exam, or maybe not, I wonder, oh, I don't know, maybe, oh, I don't know, okay, it remembers your last 20 operations, that can be really handy for something like the quadratic formula, suppose you're doing the quadratic equation and you go bracket, negative b, 8 plus the square root of 8 squared minus 4 times a times c, I'm just making up numbers, close bracket, close bracket, all over 2a, what about 4a, if you did your quadratic equation with the plus sign, then all you do is second function, enter, backspace, backspace, backspace, change the plus to a minus, and there's your plus or minus b squared minus 4acl over 2a, very nice, or if you're in chemistry and you're doing the same mathematical operation over and over to fill in a chart, but you just need to change one number each time, second function, enter, change the number, how to graph, press y equals, right here, you might have some graphs on your screen already, if you have a y1 or a y2 or a y3, just press clear, down arrow, clear, down arrow, clear, until everything is cleared, so clear any graphs that you have there already, the other thing you want to make sure is you want to make sure that plot 1, plot 2, and plot 3 are not highlighted, if they are, just go up arrow and hit enter, that toggles highlighting on and off, you want to make sure none of them are highlighted, those are stats graphs, if they're highlighted it'll try and graph those as well, you don't want some strange graph coming out of nowhere showing up on your screen, let's do our old standard, the parabola, so y1 equals, where is the x button, you guys feel okay Holly, good, yes, or question, by the way if you fall behind or you can't do something, ask, we're good, Carly, Hailey, I said Holly twice, Hailey, sorry, Hailey, we're good, twice, yes, happy, okay, y equals, where's the x button, look up, right next to the alpha, right there, x squared, boom, right here, x squared, to graph it, hit graph, now I'm willing to bet your graph might not look like mine, it might, the reason is we have to tell the graph in calculator which area of the graph to focus on, we could have all different windows, so press the window button right here, this tells the graph in calculator how much of the screen or what dimensions of the screen to display to you, x min stands for the minimum x value, it's how far left it's going to graph, x max stands for how far right the graph is going to go, so I have my graph set up to go from negative 10 to positive 10, x school stands for my x scale, one on this graph, each hash mark is going to go up by ones, y min, this graph is going to go to negative 10, y max, this graph is going to go to positive 10, y scale, one, so if your numbers don't match mine, just type them in and hit enter as you go along to get to the next line, the only one you don't want to change is this one here, x res, don't change that, okay, if you're getting an error, if you have a question, now's the chance to ask, okay, we were good? No, yes, no, yes for sure, because otherwise you can't do the next step, you can't do that, something wonky, yes, that's what I was trying to get at, then, so now hit graph and all of our graphs look identical, yes, if they don't, now's the chance to raise your hand, good, yeah, the last important one that we're going to talk about for now is the mode button, which is right here, give or press your mode button, for math 12, you want everything in the first column to be highlighted, except right now you want to be in degrees, if you borrow a calculator, you're probably in radians, just use your cursor key to move around until degrees is highlighted and press enter to toggle it on and off, one more thing, you can make your screen lighter or darker, I don't know how your calculator is set, if you go second function down arrow, keep going second function down arrow, second function down arrow, second function down arrow, that makes your screen either lighter or darker, I can't remember what, which one does it do, lighter, go second function up arrow, until you're at a darkness that you like, all depends on how far you hold the calculator away from you and what angle, if you ever have a calculator and it's not going on, it might not be the battery, it might be so light you can't see the screen, so before you do anything else try going second function up arrow, up arrow, up arrow, bunch of thumbs, try making it darker, now keep your graphing calculators out, we're going to be using them later on, but first the homework from last day, lesson two, page 98, which ones would you like me to go over, number seven, yep any before that, this one here, someone already got the candy by the way, now I did say for 4f, this is not going to be on your test, however this trick that I'm going to show you is going to come in handy after Christmas, so let's do 4f, can you read me the hint Brett, sorry as what, not 6x, that's completely different, I got to be fussy here because I got to beat a bad habit out of you, okay, 6 to the power of x, okay, since we're doing exponents all this unit you better be fussy on the difference between the 6x and the power of x, here's what I'm going to do, temporarily I'm going to let that be a variable and replace it in here, now watch what happens before you write down, just watch what happens, look up, watch what happens, have patience, I'll pause in a second, watch what happens when I do that, now the zero stays the same, the 72 stays the same, the plus stays the same, but I'm going to write this as 74a, because 6 to the x I'm replacing with an a, and I'm going to write this as 2a squared, why a squared, well this is 6 to the 2x which is really 6 to the x all squared, I'm replacing every 6 to the x with an a, write that down, then we'll talk about why, Joran did I give you your candy for getting this one, I did, Joran was the one who already got this one so pull your socks up everybody else, you okay with that so far, what kind of an equation is this, quadratic, how do I know, it's got a squared, have I written it as a quadratic equation, replacing the 6 to the x with a variable, yes, I think the first thing that I would do is I would go divide by 2, divide by 2, divide by 2, divide by 2, and it gives me a squared minus 37a plus 36 equals 0, I'm much nicer quadratic because now Dominique there's no coefficient in the front, this factors, what are two numbers that multiplied a positive 36 and add to negative 37, Justin, I think you said, did you, negative 36 and negative 1, this factors into a minus 36, a minus 1 equals 0, what are the roots, what are the roots, now hold on, don't write this, just watch for a second, I was gonna go a equals and a equals but what's a actually, what was the substitution that I did at the very beginning, you know what I'm gonna write, here's the equations that I get out of here, 6 to the x equals 36 and 6 to the x equals 1 and I can solve these in my head, 6 to what equals 36, what does x have to be for this to be true, 6 to what power equals 36, 6 to the third is 36, 6 times 6 times 6 is 36, really, you're tired right now, everyone else, huh, yes, and a little bit of a trick question, 6 to what power equals 1, ah, there's your roots, there's your real solutions from this equation, it's a quadratic, I got two answers in disguise because it wasn't really obvious that there was a squared in there but there is a squared in there, this trick of taking something ugly and substituting it with something that gives you a prettier equation, that's the trick I want you to remember, after Christmas we'll be solving quadratic trig equations so that we'll have 2 sine squared plus 2 sine minus 5, I'm gonna replace the sines with a's and we'll solve the quadratic 2a squared plus 2a plus 5 and then bring the sine back later, easier, any before number seven, yes, this one here, yep, first of all, what base am I gonna write everything as, pretty sure, and I'm gonna do the right hand side first because I know I'm gonna get it right and it's no longer blank and I'll feel better, I know this is 3 squared, I've done half the equation, yay, and I know that this is 3 to the x plus 1, yay, and I know that this is 3 cubed to the 2x minus 1, yay, what's this thing as an exponent, cool, I now have a power to a power on the bottom and I have a power to a power to a power on the top and multiply everything, in the interest of saving space I'm gonna go three times a third first because you know what three times a third is, these guys would end up just canceling, on the top I would get three to the 2x minus 1 all over, on the bottom I would get three x times, oh fractions is the easiest it's top times top, bottom times bottom, it's x times 1 which is x 1 times it's x over 3 plus 1 over 3 equals 3 squared, now what, I'm not gonna panic I'm gonna be stubborn and clever, by the way I would consider this probably a little harder than I feel comfy on the test, now what, how would I get rid of the fractions using a math 8 trick, no, no, no, even easier than that, maybe we're not talking about the same fractions, I'm talking about the great big fraction on the left, yeah you do, what can I do here, absolutely I can do it here, it looks ugly I can still do it here, I heard it finally, what, no, I can't, no, cross multiply is this not, one fraction equals, it's one ugly fraction, yes, but it's one fraction equals one fraction, the great 8 trick still has to work, what's the bottom of this fraction over here by the way, gotta still work, cross multiply and I'll get 3 to the 2x minus 1 equals 3 squared times 3 to the x over 3 plus a third, still ugly but that definitely actually looks better, do I have one base equals one base, say no, I don't have one base, I have one base equals two bases, so you ready, do I have one base equals one base, say no, well then I better write that right-hand side as one base, what's, oh, is that a 3, is that a 3, my bases here are the same and I'm multiplying, what do I do with the exponents, add them, ah, look up, adding fractions is a bit more work, that's not a 2, it's a 2, okay, I'll drop the left side down, is there an x in here, so in terms of like terms there's gonna be an x over 3 plus 6 thirds plus 1 third, by the way have I done anything new so far, nope, stubborn clever, do I have one base equals one base, are my bases the same, then I could equate the exponents, the equation I'm gonna spend my rest of my time solving now is this bad boy, 2x minus 1 equals x over 3 plus 7 over 3, now what don't I like about this equation, fractions, grade 9 you learned a wonderful trick that can make the fractions in an equation vanish, multiply everything by the common denominator which in this case is 3, I'm gonna put little 3 right there, little 3 right there, little 3 right there, little 3 right there and the nice thing is you know what happens to these 3's Ellen and to these 3 they cancel, in fact I get this, so much fun, 6x minus 3 equals x plus 7, now what minus x from both sides all the 5x plus 3 to both sides all the 10, what's x, oh that was fun, so much fun, any others before number 7, I like 4c, I like 4c, 4c and 4d is also very very similar, okay, is this exponent on the 49, then let's move the 49 over, yeah I'm gonna do this first thing, I'm gonna write this as 7 over 12 to the 2x equals 144 over 49, what do I want to write this as, I'm pretty sure sandally since I can't break a 7 down or a 12 down it's not, they're not some number to my photo, I'm pretty sure I want to write this as right hand side as 7 over 12 to some power, problem, what's that in disguise, a 12 on top, where's the 12 here, what's this in disguise on the bottom, where would I prefer it to be, it'll be wonderful if there was some kind of mathematical operation that acted, oh I don't know, like an elevator as it were and would cause things to change levels, okay and this is 12 to the what, and this is 49 to the what, I think the whole thing is gonna look like this then, if I want to get the 7 on top and the 12 on the bottom, it can't be a 2, it's got to be a negative 2, do I have one base equals one base or my base is the same, then I can equate the exponents, 2x equals negative 2, I think x is going to get a 1 in the 7 though, little question Number is 7, 7, Dominic what am I gonna write everything as, a power of what, 5? No, 8? No, 2, yes so what's 8 written as a 2, 2 to the what, what's 1 over 8 written as a 2, okay this first one is 2 to the negative 3 to the x minus 3 equals, I'm happy with that 2, what's 16 as a 2, 2 to the 4th to the 2x plus 1, power to power, power to power, I'm gonna get 2 to the junk junk negative 3x plus 9 equals, I'm happy with that 2 there, 2 to the junk junk 8x plus 4, do I have one base equals one base, not yet, oh on the right hand side I got 2 bases, what's the base here, what's the base here, the bases are the same and I'm multiplying, what do I do with exponents when my bases are the same and I'm multiplying, what is the exponent on the 2 here it's invisible, so you're saying it's that, in fact call me silly but if I add the exponents don't I get, yes, are my bases the same, do I have one base equals one base, then I can equate the exponents, the actual equation I'm gonna solve is negative 3x plus 9 equals 8x plus 5, I think you'll get 4 equals 11x when you minus 5 from both sides plus 3x to both sides, I think you'll get x equals 4 over 11 and they want to the nearest hundred, I used to know it 4 over, is it 0.36363, okay, doesn't seem right to me, gosh I forgot I mean mixed numerals, oh it is 0.36, I'm right, wow, is that okay, once again, did I really do anything new there, nope, stubborn clever, careful, turn to lesson 3, lesson 3, the exponential function, the exponential function, now in my last class I didn't get through the whole lesson, I got through part of it, so if that happens here, we'll do two lessons on Monday which works okay anyways because the second lesson fits into this one, if you have not finished the homework from last day, you really really really really really really want to finish it because I like almost everything that I gave you last day, woman number one, Mallory who's a medical research scientist discovered a new bacteria culture which can help strengthen a person's immune system, to find the growth rate she isolated five cells of the culture and here's what she noticed, after one hour there were 10 cells, after two hours there were 20 cells, after three hours there were 40 cells, how many cells would there be after four hours, it's about the pattern, 80, okay, what's happening every hour, A says let T represent the time in hours, okay, and N of T represent the number of cells after T hours, the formula can be written like this, where T is an exponent, find the values of A and B, so as an equation what they're saying is there is an equation for which when I put in a zero I get a five back, when I put in a one I get a ten back, when I put in a two I get a twenty back, when I put in a three I get a forty back, when I put in a four I get an eighty back, can anybody spot the equation that looks like this, I always, I rarely, every once in a while I have a kid who can see it, otherwise I'll tell it to you but I always pause, anybody come up with the equation, sorry, is it a parabola, no, even weirder, so here's the equation and here's how I get it, Brett how many bacteria did I start out with, start out with that, start out with what you start out with, Brett, Brett, Brett, there's a Freudian slip, say one thing and do the other, Brett what's happening here, the growth rate is two and the T is an exponent, in fact it's not a parabola, Ellen, it's an exponential equation for the first time, T the variable is sitting up here, we looked at it a little bit last day, I'll prove to you that this works by the way, Ellen put a zero in, what's anything to the zero power, times five is, you mean zero gives you a five, yes it does, let's try putting a two in, what's two squared times five, does two give you a 20, yes it does, let's try putting a three in, what's two cubed times five, does three give you a 40, it works, that's an exponential equation, call that because the variable isn't exploding, B says use this formula to determine how many cells there were after eight hours, what they're really saying is find N when T is eight, N of eight and it's going to be straight calculator five times two to the eighth, on your calculator, on your graphing calculator, get used to it, go five times two to the eighth, can't remember where the exponent button is, find it again, we have a little hat thing, what do you get, hang on, hang on, I can do this in my head, two, four, eight, sixteen, thirty, two, sixty, four hundred, twenty-six, twenty-six times five is going to be a thousand, plus two hundred, plus two hundred and fifty, plus eight, one thousand, two hundred and eighty, after twelve hours there's twenty thousand, four hundred and eighty cells, when was there, how many hours ago, how many hours did it take to get half that many, after twelve hours there's twenty thousand, four hundred and eighty, how many hours did it take to get half that amount, you guys are smart, every year I have a bunch of kids that say six, eleven because if it doubles every hour it had half as many one hour ago, eleven, I have a little talk, I don't think I'll be able to show it in class I want to time, but the guy who's giving the talk says he argues one of the biggest issues in society, one of the biggest reasons that we are so terrible at planning the future is we don't have a good understanding of how exponential growth works, put your pencils down and look up, let's suppose this is the earth, there's the earth and let's suppose right now, let's suppose that the population is that big, we have a huge amount of room, you want to burn some oil go ahead, you want to make some landfills, pile up some garbage, go ahead we got lots of room, you want to fish the oceans, go ahead and the population doubles, still lots of room, still lots of room, we would have most people because they'd understand exponential growth works, they'd be saying oh for a pizza, it's global warming, are you stupid, look at all the room, please, we double one more time, we got a problem, we've run out of everything, most of the experts that I've read think we're here right now and sometime in the next 20 years, you're starting to see bits of it already, have gas prices gone way up in the past 10 years, yeah more people and more cars, electricity a couple of years ago California was actually having rolling blackouts, so your town wouldn't have power for two hours at certain times of the day because they were running out, but 10 years ago California was get more air conditioners, lots of room, build more houses, lots of room, we don't understand how exponential growth works, far too many citizens, far too many politicians for part C would answer oh six hours ago, lots of time, lots of time, D says use a graphing calculator to graph this, okay get your graphing calculators out, press y equals and clear whatever equation you got there, now I want to graph this, my calculator does not have an n, instead I've got to put a y there, my calculator does not have a t, what letter am I going to put there instead, x, I'll adjust, so I'm going to go five times two to the power of and I'm going to press my x button, now if you hit graph you're going to get some nonsense, nothing terribly entertaining, we want to adjust this window, so press window, now remember x is actually time, look at my chart, what's the smallest amount of time that appears in my chart, so I'm going to let x min be zero, what's the maximum amount of time that this question mentions anywhere, not three, what's the maximum amount of time this question mentions anywhere in the question, when I get the whole thing on there, 12, I think going up by ones there would work okay because 12 hash marks in an area of screen that long should be okay, so scale one, now y is the number of bacteria, what's the fewest number of bacteria that this question mentions, five, I could go five, I like to see zeros, I'm actually going to start out at zero high, I always like to see the x axis, what's the largest number of bacteria that this question mentions, 20,480, so I'm going to go to a nice roundish number, I'm going to go to 21,000, if I'm going from zero to 21,000 to the space this big, would a scale of one make, going up by ones with hash marks make much sense, Kara's shaking her head, like you know what Kara, I'm going to let my scale be about 5,000, now hit graph, all of our graphs should now look the same, and we should be able to see way more stuff going on, is there anybody who didn't get that now is your chance to ask, usually it means a little typo, I can fix it right away, as the graph, it looks like this, the further right you go, the steeper it gets, the further left you go, the closer it gets to zero, but never quite touches, in fact the x axis is a horizontal asymptote, looks like this, if we get our disco now, because it's getting bigger as we move to the right, we call it exponential growth, you know what an exponential decay graph looks like, gets smaller as we move to the right, Chernobyl is a city in the former Soviet Union, what happened at Chernobyl, why is Chernobyl famous, Eric, more specific there are plenty of places that have nuclear power plants that aren't famous, what happened at Chernobyl, sorry didn't blow up, didn't actually leak, a leak is like, ah but it had a complete core meltdown, it had a nuclear meltdown, the worst nuclear power plant disaster that we've had, it happened in the height of the cold war, and so the Russians at that time denied it, all the world nations were detecting in 1986 a huge radioactive cloud circled the planet three or four times before it finally faded into nothingness, and all of our instruments were detecting it, and when we traced our way backwards to the cloud's origin it kept starting somewhere in central Russia, so we, the US, Canada, all the countries phoned Russia and said you've got a problem, Russia said yes, you don't, finally after a couple of weeks they fessed up and they admitted yeah we've had a very, very serious nuclear reactor meltdown, if you want to read just a tragic story google chernobyl and just find how horrible it was because the way they fixed it was they sent, they ordered soldiers to their death, for example they couldn't get the fire to stop, so they flew helicopters and dropped liquid concrete from the helicopters into the reactor, the pilots all died horrible deaths a couple of months later of radiation, even to this day people that live in the area have a high incidence of leukemia, kids in that area are born without, with birth defects, they moved the town of Chernobyl, but there are still some people that live there, horrible the way it was handled, so it was partly the fact that it was a nuclear meltdown and probably the fact that they botched it so badly, the one that happened that almost happened in Japan with the earthquake, nothing compared to this, I don't think that Japan will need much radiation at all, so radiation, radioactive, radiation decays, radioactivity decays, now again just like in the previous question Carly, we've cooked the numbers to make the numbers nice mathematically because I'm going to tell you that cells don't divide, don't multiply by two on every single hour, they would multiply by 1.67 every three hours, 43 minutes and 19 seconds, like you never get nice numbers like that, they've done the same thing here, so it says initially they measured 32,768 units of radioactive iodine, after one week there was that many, two weeks there was that many, two weeks there was that many, what's the pattern here, someone said something I think, what's the pattern, what's going on here, Justin, did you say it, I like the way you said it, almost every year people say dividing by two and I say well I don't want to divide because here I multiplied instead of dividing by two, what number would I multiply by, but you said it right away, yeah as it turns out the growth rate here is a half, says use the formula to determine how many units of radioactive iodine were left after 14 weeks, they want me to find n of 14, I'm going to go, 30, oh turn my calculator around, clear clear clear to get out of the graph menu, 32,768 times bracket, one half closed bracket to the power of, it says two, this is how I know they cook these answers, these are fake answers, but okay, paradigm, use a graphing calculator to graph this, okay y equals, clear the equation you have there and the equation is this bad boy, so 32,768 times bracket, one half closed bracket to the power of, oh I can't do t, what am I going to do instead, x, where's the x, oh yeah, right there Henry, oh except they also gave me the view window that they want me to use so that all of our graphs look the same, so press window and carefully type in this view window, I guess on the y axis we're going to go up by 10,000 which makes sense, once you do that hit graph and you should get a decay graph, a graph that starts up steep and gets shallower and shallower and closer and closer and closer, like that, like this, some handy features, how much iodine is left after five weeks, don't type it in, instead you have the graph in front of you, press the trace button right here and once you press the trace button a little cursor should appear and what that's saying is you can use your left and right arrows to move around and it gives you y values that go with, so after five weeks I can get 4.936 weeks and I can get 5.03131949 weeks, there's a better way to trace, so you're all in the trace menu, instead type 5, if you type the number 5 when you're in the trace menu at the bottom x equals appears hit enter, oh after five weeks how much iodine was left, 1024 after seven weeks how much iodine was left, 256 after 10 weeks how much iodine was left, you get an error, why, what's the biggest x value that I was graphing, eight I'd have to change my window if I wanted to get the 10 maybe easy enough to do, sometimes if I'm doing the same equation over and over and over and over and over but just with different numbers like maybe in chemistry I type the equation, oh go to, I type the equation in here pick a big window and just use my trace feature it's nice we call this exponential decay turn the page exponential functions an exponential function is an equation that looks like that where the x is an exponent where b is the base, b is the base, b is the base, I wonder how I can remember that b is the base and a is the coefficient in fact Trevor a is a vertical stretch if I go back to last unit and it could even be a vertical reflection if I go back to last unit we have to add a couple of restrictions though a can't be zero why can't a be zero if a was zero I'd have zero times b to the x what's zero times anything that's not going to give me this shape guarantee it oh and we add one more thing b has to be positive you can't have a negative base put pencils down here's why you couldn't have this don't write this down when this was even your answer would be positive when this was odd your answer would be you'd have a graph that was positive the negative positive negative positive negative positive I guarantee that's not giving you this shape that's jumping all over the place what would that graph look like try it on your calculator if you board sometimes oh let's try that right now just because y equals clear clear clear negative three to the power to the power of x I'd like look up here's your next shortcut which is why I'm doing this I want to graph from negative 10 to positive 10 from negative 10 to positive 10 it's such a handy window if you press zoom these are built in windows and zoom standard option six gives you negative 10 to positive 10 negative 10 to positive 10 what appeared your calculator doesn't even know how to graph it maybe that's too big let's try a smaller number your calculator doesn't even know how to graph it so the base has to be positive let's look at two graphs and we're going to do these in our head we're going to compare two to the x and one half to the x we're going to do these pencil and paper not with technology first thing it says is state the values of a and b for both of these graphs what's a here it's not two it's the number in front what number is in front here it's invisible and also a equals one here in other words we're saying look ignore vertical stretches while we start you out what's be the base here to what's be the base here b says sketch the graph of two to the x so I'm going to graph y equals two to the x and the way I'm going to do that is I'm going to plug in numbers and I always start with zero what's two to the zero zero goes with one on the graph zero goes with one zero comma one is a point what's two to the one when x is one y is two what's two to the two when x is two y is is what four two over four up what's two to the third when x is three y is a four five six seven eight what's two to the fourth two times two times sixteen off my graph forget it let's go in the other direction what's two to the negative one elevator one over two what's two to the negative two elevator one over four what's two to the negative three elevator one over eight now I can't graph negative three comma one eighth very easily I can't graph negative two comma one quarter very easily I can and graph negative one comma a half and this gives us the shape. It looks like that. Eric, you know what it looks like? Put your pencils down, Eric. Looks like this. Looks like this. Can you do that with your hands, Eric? One hand here and one hand here. Disco man. Oh, you might hit Brianna in the head accidentally. That's just a risk she's gonna take. Okay? So you got that? I'll be picking on you all day, all year for this one. I don't have a basketball player in the back row. Could go with Trevor. Doesn't got long arms. Okay, hands back down. Let's graph this next one. I'm gonna do this in red. Y equals one half to the X. And like always, I start out with zero. What's any of them to the zero power? One, right? What's one half to the one? A half? What's one half squared? Okay, we're getting smaller. Let's go in the other direction. What's one half to the negative one? What's the elevator when the fraction's already on the bottom? It's gonna make it... What's one half to the negative one? Two. And you know what one half to the negative two is? Four. Keep the pattern going. Eight. This is gonna go through negative three, eight high. Negative two, four high. Negative one, two high. Zero, one high. In fact, I can't look like that. Eric, my friends, are you penciled down? Every single exponential graph looks like this or like this. Do that for me, please. Lean forwards. Like this. Lean forwards. Or like this. Slide forwards. The chair forwards. Every exponential graph looks like this or like this. Like this or like this. You're supposed to hit them in the heads, Eric. No, as a graph, okay? Now it works. It's your one chance to smack somebody up the head.  Don't write this down, but watch, watch, watch, watch, watch, watch, watch. Look, look, look, look, look. Is this true? Is one half to the X the same as that? Why? You're right. It is the same. Why? Where the negative come from? Oh, elevator. Look at this, look at this, look at this. Didn't I replace X with negative X? Isn't that a horizontal reflection? Oh, there's another way to think about it. Instead of fractions, you can think about it as, it's actually a horizontal reflection, which it is. It's a nice tie-in with last unit, whatever. Here's what I want you to notice. Here's what they have in common. Eric, what does every single exponential graph look like? Come on, come on. This is your cue every time, buddy. Don't let me down here, here or? What's the domain right now? By the way, not straight up, curving up, right? Getting steeper, yes. Not this though, this levels. Okay, what's your domain? Point, sorry? What's the domain of Eric? What's the domain of this? We've never said infinity all year, what we called that. So in this chart, put your hands down now, Eric. Domain, all reels, and it's the same for both of them. So I'm just gonna write it big and put it in both. What's the range? How high do these graphs go? Forever, how low do these graphs go? Zero, but not touching, closer and closer to zero. Everything above, but not touching zero. How will I write that? Everything above zero, but not touching, so no or equal to. What's the x-intercept of an exponential graph? It's a trick question. An x-intercept of an exponential graph. It's a trick question, isn't it one? It gets closer and closer and closer and closer and closer and closer and closer and closer and closer and closer and closer to the x-axis, never touches. What's the y-intercept of an exponential graph? Zero comma one. And what I said to you earlier was, both of these graphs have as an asymptote, the x-axis, what's the equation of the x-axis align horizontally zero high? Nice, y equals zero. That is true of every single exponential graph that doesn't have a coefficient for anything else done to it.  On Monday, I'm going to introduce you to the log graph, the logarithmic graph. You know what, all I'm gonna tell you is it's the inverse of the exponential. It's the inverse of the exponential. So just by telling you that and looking at this chart, you ready? If logs are inverses of exponential, what's the domain of every log graph? What's about it? X is greater than zero, because the range is gonna become a domain, it's what's x and y. You know what the range of every log graph is? Oh, what's the x-intercept of a log graph? One comma zero, it's the y-intercept. Does it have any y-intercepts? Nope, does it have an asymptote? Yes, vertical asymptote, no. Horizontal asymptote? Sorry, horizontal asymptote, no. Has a vertical asymptote, y equals zero. So even though you've never met the graph, you've seen parts of it before. You have to go earlier or something? Okay. Oh. Growth decay. Dear Mr. Dewitt, you are my favorite math teacher. I've attached $5 here, excellent. Turn the page. What do you think happens as my base gets bigger? Let's find out, get your calculators out. We're gonna do three equations. So clear, clear everything, and go zoom standard right away so that our window is the same. Zoom button, option six. Now here are the three we're going to graph. Two to the power of x, enter. Three to the power of x, enter. And then five to the power of x, enter. But before we hit graph, I'm gonna show you a few more things you can do. You see, if we graph these, they're all gonna look the same. If you go up arrow and to the left of y2 with your cursor, so that you're right here, and you hit enter once, that makes this graph a thick line, so you can tell it apart. If you go down arrow, so that you're to the left of y3, enter once would make it a thick line, we already got that. Enter again, colors everything above the graph, I don't wanna do that. Enter again, colors everything below the graph, I don't wanna do that. What I do want is this one, which is a follow the bouncing ball. Now hit graph. There's two to the x, there's three to the x, there's four to the x. As this number gets bigger, what happens to the steepness? Get steeped, which makes sense. Here's what you need to memorize. For any exponential function without a vertical stretch, with no a, x intercept, none, y intercept, zero comma one, domain, all reels, range, everything above, not touching zero, equation of the asymptote, y equals zero. So the page, warmup number five, wants us to explore what happens when you put an a in front. I already know that's a vertical stretch. So if normally my y intercept is zero comma one, what would the y intercept of this one be? What's my vertical stretch right here? It's a vertical stretch by a factor of two, it'll be zero comma two. In fact, turn the page, page 105. This is the page we want to be on. The y intercept is normally zero comma a. Oh, and if a is one, like the first bunch that we looked at is zero comma one. There is blank x intercept. There is blank x intercept. What word goes there? No x intercept. The x-axis is a horizontal asymptote. The domain is all reels, and the range is everything above zero. Reminder for Halloween for 100 straight drives may end in three. Cringes plus non-perishable to run, you can do your block A cost. If you have a straighter, bring them to Mr. and Classroom. The winning home. Cringes plus non-perishable to run, you can do your block A cost.