Chapter 8.5, Problem 23SR

(a)

To determine

To find: the rate of change

Answer to Problem 23SR

The rate of change is $\$12$

Explanation of Solution

Given:

Water Park Costs
Number of People	Total Cost $\left(\$\right)$
$x$	$y$
$3$	$36$
$4$	$48$
$5$	$60$

Calculation:

The objective is to find the rate of change and interpret its meaning.

First, plot a graph for cost $(\$)$ on $y-axis$ and the number of people on x-axis.

  

The graph is a straight line; choose any two the points on the line, say $(3,36)$ and $(4,48)$ to find the rate of change.

The rate of change will be given by:

  $\begin{array}{l}Rateofchange=\frac{Changeincost\left(\$\right)}{Changeinnumberofpeople}\\ =\frac{48-36}{4-3}[Simplify]\\ =12\end{array}$

The rate of change is $\$12$ per person. This implies that, it costs $\$12$ for a person to enter the water park.

Conclusion:

Therefore, the rate of change is $\$12$

(b)

To determine

To find: the meaning of rate

Answer to Problem 23SR

The rate of change is $\$12$ per person. This implies that, it costs $\$12$ for a person to enter the water park.

Explanation of Solution

The rate of change is $\$12$ per person. This implies that, it costs $\$12$ for a person to enter the water park.