Chapter 4.5, Problem 88E

Big Brother The following chart shows the total number of wiretaps authorized each year by U.S. state courts from 1990 to 2013. ( $t=0$ represents1990.)⁴⁵ N(t) Wiretap orders, state counts only

These data can be approximated by the model

$N\left(t\right)=410e^{0.071t}\left(0\le t\le 23\right)$

a. Find $N\left(20\right)\text{ and }N\text{'}\left(20\right)$. Be sure to state the units of measurement. To how many significant digits should we round the answers? Why?

b. The number of people whose communications are intercepted averages around 100 per wiretap order. What does the answer to part (a) tell you about the number of people whose communications were intercepted?

c. According to the model, the number of wiretap orders each year (choose one)

(A) increased at a linear rate

(B) decreased at a quadratic rate

(C) increased at an exponential rate

(D) increased at a logarithmic rate over the period shown.