The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, 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

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The water usage at a car wash is modelled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.

The amount of decrease in water used is modelled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find what

C(x) = W(x) - D(x)

C(x) = ( 4x³ + 6x² − 11x + 7, ) - ( x³ + 2x² + 15 )

C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15

C(x) = 3x³ + 4x² - 11x - 8

Therefore A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8

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