Chapter 8, Problem 25SGR

To determine

To compare: the rates of change.

Answer to Problem 25SGR

Rate of change for adult is increase of $18 per person

The rate of change for children is increase of $12.5 per person

Explanation of Solution

Given:

Number of People x	Total Costs ($) y
	Adults	Children
2	36	25
4	72	50
6	108	75

Calculation:

The rate of change is change in one quantity with respect to another quantity. Mathematically:

  $\text{Rate of change }=\frac{\text{change}\text{in}y}{\text{change}\text{in}x}$

Thus, the rate of change is change in total cost with respect to change in number of people.

So, the rate of change for adult is:

  $\begin{array}{c}\text{Rate of change }=\frac{72-36}{4-2}\\ =\frac{36}{2}\\ =18\end{array}$

And, the rate of change for children is:

  $\begin{array}{c}\text{Rate of change }=\frac{50-25}{4-2}\\ =\frac{25}{2}\\ =12.5\end{array}$

It means that the cost for adults increase at faster rate than the cost for children.

Conclusion:

Therefore, Rate of change for adult is increase of $18 per person

The rate of change for children is increase of $12.5 per person