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

$25.5 per hour.

Explanation:

The function C(x) = 25.50x + 50 ........ (1) 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.

Now, from the linear equation it is clear that the change in cost of cleaning from 3 hours and 9 hours are respectively {From equation (1)}

C(3) = 25.5 × 3 + 50 = $126.5 and

C(9) = 25.5 × 9 + 50 = $279.5

Therefore, the average rate of change of the function between 3 hours and 9 hours will be =
`\frac{\textrm {Change in price of cleaning}}{\textrm {Change in hours}}`

=
`(279.5 - 126.5)/(9 - 3)`

= $25.5 per hour. (Answer)