Question

The water usage at a car wash is modeled by the equation W(x) = 3x^3 + 4x^2 − 18x + 4, 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) = x^3 + 2x^2 + 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.

Answer 1

C(x) = 2x^3 + 2x^2 - 18x - 11

Explanation:

Step 1: To model the water used by the car wash on a shorter day, we can subtract the amount of water saved from the original water usage function.

Step 2: Therefore, we can define the new function C(x) as: C(x) = W(x) - D(x)

Step 3: Substituting the given functions for W(x) and D(x), we get: C(x) = (3x^3 + 4x^2 - 18x + 4) - (x^3 + 2x^2 + 15)

3x^3 + 4x^2 - 18x + 4 -x^3 - 2x^3 - 15

Step 4: Simplifying by combining like terms, we get:

C(x) = 2x^3 + 2x^2 - 18x - 11

Step 5: Therefore, the function C(x) that models the water used by the car wash on a shorter day is: C(x) = 2x^3 + 2x^2 - 18x - 11