Chapter 11.5, Problem 87E

(a)

To determine

To calculate: The value of $N\left(15\right)$ and $N^{\prime }\left(15\right)$ when the approximated model is given by $N\left(t\right)=770e^{0.060t}$ where t is the time since $1990$ $\left(0\le t\le 23\right)$ and also round off the answer to significant digits with providing a reason for that. The total number of the wiretaps authorized by U.S. state and federal courts each year during $1990-2013$ is given by the graph as,

(b)

To determine

The interpretation about the number of people whose communication were disturbed from the answer of part (a) when the number of people whose communication were disturbed averages around $100$ per wiretap order.

(c)

To determine

The nature of variation in the number of wiretap orders over the period $\left(0\le t\le 23\right)$ as per the model that is approximated as $N\left(t\right)=770e^{0.060t}$ from the following options:

(A) Increased at a linear rate.

(B) Decreased at a quadratic rate.

(C) Increased at an exponential rate.

(D) Increased at a logarithmic rate.