Chapter 8.6, Problem 32E

(a)

To determine

To Find: The comparison for the population of the town and then interpret the average rate of change from 1990 to 2010.

Answer to Problem 32E

The average rate of change is 950.5. The average rate of change are the rate of increase of the population from 1990 to 2010.

Explanation of Solution

Given:

The population of the town increases A increases by 20% every decade.

The $x$ shows the number of decades since 1970.

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the town A is modelled by $a={\left(1+r\right)}^t$ where $a=3000$ , $r=0.2$ then,

  $a={\left(1+r\right)}^t$

Then, the equation is,

  $y=3000{\left(1.2\right)}^t$

For year 1990.

  $\begin{array}{c}y=3000{\left(1.2\right)}^2\\ =1320\end{array}$

For year 2010.

  $\begin{array}{c}y=3000{\left(1.2\right)}^4\\ =6221\end{array}$

Then, the average rate of change is,

  $\frac{6221-4320}{4-2}=950.5$

(b)

To determine

To Find: The prediction for the two that have greater population after 2030.

Answer to Problem 32E

The town A will have larger population in 2030.

Explanation of Solution

Given:

The given equation is $ax+b=cx+d$ .

The student A claim that the equation will have only one solution.

The student B claims that the equation will have no solution.

Calculation:

From the rate of change in part (a) the town A will have larger population in 2030.