The temperature $T$ of a cup of coffee, in degrees Fahrenheit, is modeled by $T(t) = 70 + 80e^{-0.2t}$, where $t$ is the time in minutes since it was brewed. What is the average rate of change of the temperature between $t=2$ and $t=5$?

Core Concept

The average rate of change over an interval is found by evaluating $\frac{T(5) - T(2)}{5 - 2}$. Substituting the values yields $\frac{70 + 80e^{-1} - (70 + 80e^{-0.4})}{3}$, which correctly simplifies to this expression.