Chapter 8.1, Problem 84E

Prison Population The number of prisoners in state prisons in the United States can be approximated by

$N\left(x,y\right)=-540+7.5x+2.5y-0.01xy$ thousand inmates, where x is the number, in thousands, in federal prisons and y is the number, in thousands, in local jails.⁷

a. In 2010 there were approximately 198 thousand prisoners in federal prisons and 749 thousand in local jails. Estimate, to the nearest 0.1 million, the number of prisoners in state prisons that year.

b. Obtain N as a function of y for $x=80$ and again for $x=100$. Interpret the slopes of the resulting linear functions.