Chapter 3.5, Problem 83E

Prison Population The following curve is a model of the total U.S. prison population as a function of time in years.

Time (year since 2000)

a. Which is correct? Over the period $\left[5,10\right]$ theinstantaneous rate of change of N is

(A) increasing. (B) decreasing.

b. Which is correct? The instantaneous rate of change of prison population at $t=4$

was

(A) less than (B) greater than

(C) approximately equal to the average rate of change over the interval $\left[0,10\right]$.

c. Which is correct? Over the period $\left[0,10\right]$ theinstantaneous rate of change N is

(A) increasing, then decreasing.

(B) decreasing, then increasing.

(C) always increasing.

(D) always decreasing.

d. According to the model, the U.S. prison population was increasing fastest around what year?

e. Roughly estimate the instantaneous rate of change of N at $t=4$ byusing a balanced difference quotient with $h=1.5$. Interpret the result