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Law of cooling and Exponential growth

  1. Oct 9, 2007 #1
    A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the temperature is 75 degrees F. When will the turkey have cooled to 100 degrees F?

    2. Relevant equations
    dT/dt=k(T-Ts) where Ts=temperature of the surrounding

    3. The attempt at a solution
    I solved T(t)=75+110e^(ln .682)t/30

    Solving for t:
    100=75+110e^(ln .682)t/30

    I know that t=10 isn't right, but I don't know what I did wrong. Any takers?
  2. jcsd
  3. Oct 9, 2007 #2
    How did you solve for k?

    Just quickly I got:

  4. Oct 9, 2007 #3
    To solve for k I used the fact that y(30)=150-75=75
    So, 110e^30k=75
    30k=ln .682
    k= ln .682/30
  5. Oct 10, 2007 #4


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    Staff Emeritus
    Science Advisor

    And how did you know that y(30)= 75? You didn't tell us anything about the temperature of the turkey 30 minutes after being take out of the oven!

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