Chapter 4.3, Problem 88E

Oil Imports from Mexico Daily oil production in Mexico and daily U.S. oil imports from Mexico during 2000– 2004 could be approximated by

$\begin{array}{l}P\left(t\right)=3.0+0.13t\text{ million barrels }\left(0\le t\le 4\right)\\ I\left(t\right)=1.4+0.06t\text{ million barrels }\left(0\le t\le 4\right),\end{array}$ where t is time in years since the start of 2000.

a. What are represented by the function $P\left(t\right)-I\left(t\right)$ and $I\left(t\right)/P\left(t\right)?$

b. Compute ${\frac{d}{dt}\left[\frac{I\left(t\right)}{P\left(t\right)}\right]|}_{t=3}$ totwo significant digits. What does the answer tell you about oil imports from Mexico?