1. ## Temperature problem

Problem:

Original temperature of hot chocolate is 81 degrees. After 6 minutes in a 14-degree environment the hot chocolate is 63 degrees. Find the formula to represent the rate at which the temperature of the hot chocolate is decreasing. Also find the temperature of the hot chocolate after 15 minutes.

Any help is appreciated. And please explain if you can.

2. Originally Posted by IfUAin1stUrLast
Problem:

Original temperature of hot chocolate is 81 degrees. After 6 minutes in a 14-degree environment the hot chocolate is 63 degrees. Find the formula to represent the rate at which the temperature of the hot chocolate is decreasing. Also find the temperature of the hot chocolate after 15 minutes.

Any help is appreciated. And please explain if you can.
We have $\displaystyle T' = -k(T - T_{amb}) \implies T = Ae^{-kt} + T_{amb}$

where $\displaystyle T$ is the temperature at time $\displaystyle t$, $\displaystyle T_{amb}$ is the ambient (surrounding) temperature, which is 14 here, and $\displaystyle A$ and $\displaystyle k$ are constants (see post #2 here)

We are told $\displaystyle T(0) = 81$ and $\displaystyle T(6) = 63$. this is enough information to find $\displaystyle A$ and $\displaystyle k$. And thus answer the rest of the question