Chapter 4.4, Problem 16Q

(a)

To determine

To sketch: a graph of the function for the interval $0\le t\le 20$ using graphing calculator, and to describe the behavior of the graph on this interval.

Explanation of Solution

Given information:

The estimated price $P$ of stamps in the United States can be modeled by the polynomial function $P\left(t\right)=0.007t^3-0.16t^2+1t+17$ , where $t$ represents the number of years since 1990.

Calculation:

Input the function $Y_1=0.007X^3-0.16X^2+X+17$ using key.

  $0.007X\wedge 3-0.16X{x}^2+X+17$

The display is shown below:

  

Press the GRAPH key

  

(b)

To determine

To find: the average rate of change in the price of stamps from 1990 to 2010.

Answer to Problem 16Q

The average rate of change is 0.6 cent per year.

Explanation of Solution

Given information:

The estimated price $P$ of stamps in the United States can be modeled by the polynomial function $P\left(t\right)=0.007t^3-0.16t^2+1t+17$ , where $t$ represents the number of years since 1990.

Calculation:

The years 1990 and 2010 correspond to $t=0$ and $t=20$ .

  $\begin{array}{c}\frac{P\left(20\right)-P\left(0\right)}{20-0}=\frac{0.007{\left(20\right)}^3-0.16{\left(20\right)}^2+20+17-17}{20}\\ =\frac{29-17}{20}\\ =0.6\end{array}$

Therefore, the average rate of change is 0.6 cent per year.