Question

The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6

Answer 1

To model the water used by the car wash on a shorter day, we need to find the difference between the water usage over a full day and the water usage over a reduced day (i.e., with the car wash closed for two hours less than it would be on a full day). Let the number of hours the car wash is open on a full day be x hours. Then the amount of water used on a full day would be W(x). And the amount of water used on the reduced day (i.e., with the car wash closed for two hours less than on a full day) would be C(x). Therefore, we have:


W(x) - C(x) = 2(W(x) - C(x))


Solving this equation for C(x), we get:


C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)


Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)