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 subtract the decrease in water used from the original amount of water used. Therefore, the function C(x) is:

C(x) = W(x) - D(x)
C(x) = (5x^3 + 9x^2 - 14x + 9) - (x^3 + 2x^2 + 15)
C(x) = 5x^3 + 9x^2 - 14x + 9 - x^3 - 2x^2 - 15
C(x) = 4x^3 + 7x^2 - 14x - 6

Therefore, the function that models the water used by the car wash on a shorter day is C(x) = 4x^3 + 7x^2 - 14x - 6.