question: Esteban's account balance can be modeled by $f(t)=1000 \cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?
  Round your answer to the nearest integer. 
  
query_wo: Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
  Question: Esteban's account balance can be modeled by $f(t)=1000 \cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?
  Round your answer to the nearest integer. 
  
query_cot: Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
  Question: Esteban's account balance can be modeled by $f(t)=1000 \cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?
  Round your answer to the nearest integer. 
  
question_for_eval: Esteban's account balance can be modeled by $f(t)=1000 \cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?
  Round your answer to the nearest integer. 
  