Chapter 11.3, Problem 87E

(a)

To determine

The meaning of the functions $P\left(t\right)-I\left(t\right)$ and $\frac{I\left(t\right)}{P\left(t\right)}$ where daily oil production in Mexico and U.S daily oil imports from Mexico during $2000\text{ to }2013$ is represented by the functions $P\left(t\right)=3.1-0.014t$ million barrels and $I\left(t\right)=1.7-0.063t$ million barrels respectively where t is time in years starting from $2000$ and lies in the range $9\le t\le 13$.

(b)

To determine

To calculate: The derivative ${\frac{d}{dt}\left[\frac{I\left(t\right)}{P\left(t\right)}\right]|}_{t=11}$ to two significant digits where daily oil production in Mexico and U.S. daily oil imports from Mexico during $2000\text{ to }2013$ is represented by the functions $P\left(t\right)=3.1-0.014t$ million barrels and $I\left(t\right)=1.7-0.063t$ million barrels respectively where t is time in years starting from $2000$ and lies in the range $9\le t\le 13$. Interpret the answers.