Chapter 2.4, Problem 119E

Business: U.S. oil production. One model of oil production in the United States is given by

$P\left(t\right)=0.0000000219t^4-0.0000167t^3+0.00155t^2+0.002t+0.22,0\le t\le 110,$ where $P\left(t\right)$ is the number of barrels of oil, in billions, produced in a year, t years after 1910. (Source: Beyond Oil, by Kenneth S. Deffeyes, p. 41, Hill and Wang, New York, 2005.)

a. According to this model, what is the absolute maximum amount of oil produced in the United States and in what year did that production occur?

b. According to this model, at what rate was United States oil production declining in 2010 and in 2015?