Chapter 14.1, Problem 63E

Oil Production in Mexico The rate of crude oil production from 2008 to 2013 by Pemex, Mexico’s national oil company, can be approximated by

$\begin{array}{l}q\left(t\right)=6.2t^2-146t+1,910\text{ million barrels per year}\\ \left(8\le t\le 13\right),\end{array}$ where t is time in years since the start of 2000.⁸ During that time, the price of oil was approximately⁹

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

Obtain an expression for Pemex’s total oil revenue $R\left(x\right)$ from the start of 2008 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 $=p\left(t\right)q\left(t\right)$.]