help solve the answers from the function given

Question

The cost​ C, in​ dollars, of renting a moving truck for a day is given by the function C(x)=0.20x+45, where x is the number of miles driven.

​(a) What is the cost if a person drives x=240 miles?

​(b) If the cost of renting the moving truck is $180​, how many miles did the person​ drive?

​(c) Suppose that a person wants the cost to be no more than ​$200. What is the maximum number of miles the person can​ drive?

​(d) What is the implied domain of​ C?

​(e) Interpret the slope.

​(f) Interpret the​ y-intercept.

Answer 1

(a) x= 240 miles

C = 0.20x + 45

C = 0.20(240) + 45

C = $93

(b) C=$180

C = 0.20x + 45

180 = 0.20x + 45

180 - 45 = 0.20x

x = 675

675 miles driven

(c) Substituting C=200 in the equation

200 = 0.20x + 45

200 - 45 = 0.20x

x = 775

Maximum number of miles is 775

(d) x is the number of miles driven and will always be greater than or equal to 0.

Hence, domain is x is greater than and equal to zero.

(e) the slope is cost of each mile driven.

(f) y intercept is the cost when the miles driven are zero. Hence, it can be considered as the base cost which doesn't depend on the number of miles driven.