Question

The function C(x) = 25.50x + 50 models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house. What is the average rate of change of the function between 3 hours and 9 hours? A. $17.00 per hour B. $25.50 per hour C. $31.05 per hour D. $42.15 per hour

Answer 1

Answer:

The average rate of change is $25.5 per hour, option B.

Step-by-step explanation:

Average Rate of Change

When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from $x=x_1$ to $x=x_2$. It can be computed as the slope of a line .

$\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}$

The provided function is

$C(x)=25.50x + 50$

We are required to compute the average rate of change between the points

$x_1=3\ ,\ x_2=9$

Let's compute

$C(3)=25.50(3) + 50=126.5$

$C(9)=25.50(9) + 50=279.5$

$\displaystyle m=\frac{279.5-126.5}{9-3}$

$\displaystyle m=\frac{153}{6}=25.5$

The average rate of change is $25.5 per hour, option B.