Chapter 14.1, Problem 64E

Oil Imports from Mexico The rate of crude oil imports to the United States from Mexico from 2009 to 2013 can be approximated by

$\begin{array}{l}r\left(t\right)=-14t^2+292t-1,100\text{ million barrels per year}\\ \left(9\le t\le 13\right),\end{array}$ where t is time in years since the start of 2000.¹⁰ During that time, the price of oil was approximately¹¹

$p\left(t\right)=48e^{0.046t}\text{ dollars per barrel}$

Obtain an expression for the total oil revenue $R\left(x\right)$

Mexico earned from the United States from the start of 2009 to the start of year x as a function of x. (Do not simplify the answer; round all coefficients to three significant digits.) [HINT: Rate of revenue $=p\left(t\right)r\left(t\right)$.]