Chapter 5.1, Problem 3P

Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.

To determine

To calculate : rate of change if it is constant. Also, to find what rate of change represents.

Answer to Problem 3P

Rate of change is 4.

It represents change in number of cars washed with respect to increase in number of hours.

Explanation of Solution

Given information:

The following table is given:

Hours	Cars
1	4
2	8
3	12
4	16

Formula used: For two points $\left(x_1,y_1\right),\left(x_2,y_2\right)$ , rate of change is given by $\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Hours	Cars
1 $(x_1)$	4 $(y_1)$
2 $(x_2)$	8 $(y_2)$
3 $(x_3)$	12 $(y_3)$
4 $(x_4)$	16 $(y_4)$

Take $\left(x_1,y_1\right)=\left(1,4\right),\left(x_2,y_2\right)=\left(2,8\right)$

So,

Rate of change $(R_1)=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{2-1}=\frac{4}{1}=4$

Take $\left(x_2,y_2\right)=\left(2,8\right),\left(x_3,y_3\right)=\left(3,12\right)$

So,

Rate of change $(R_2)=\frac{y_3-y_2}{x_3-x_2}=\frac{12-8}{3-2}=\frac{4}{1}=4$

Take $\left(x_{13},y_3\right)=\left(3,12\right),\left(x_4,y_4\right)=\left(4,16\right)$

So,

Rate of change $(R_3)=\frac{y_4-y_3}{x_4-x_3}=\frac{16-12}{4-3}=\frac{4}{1}=4$

As $R_1=R_2=R_3$ , rate of change is constant.

Hence,

Rate of change $=R_1=R_2=R_3=4$

Also, rate of change represents change in number of cars washed with respect to increase in number of hours.