Exercise 6

A cup of coffee has its temperature $F$ (in degrees Fahrenheit) at time $t$ given by the function $F(t) = 75 + 110 e^{-0.05t}$, where time is measured in minutes.

1. Use a central difference with $h = 0.01$ to estimate the value of $F'(10)$.

2. What are the units on the value of $F'(10)$ that you computed in (a)? What is the practical meaning of the value of $F'(10)$?

3. Which do you expect to be greater: $F'(10)$ or $F'(20)$? Why?

4. Write a sentence that describes the behavior of the function $y = F'(t)$ on the time interval $0 \le t \le 30$. How do you think its graph will look? Why?