Question

The cost​ C, in​ dollars, of renting a moving truck for a day is given by the function

Upper C left parenthesis x right parenthesis equals 0.25 x plus 40 comma

where x is the number of miles driven.

​(a) What is the cost if a person drives

x equals 200

​miles?

​(b) If the cost of renting the moving truck is

​$150

​,

how many miles did the person​ drive?

​(c) Suppose that a person wants the cost to be no more than

​$120

.

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

C(x) = 0.25x + 40

a)
C(x) = 0.25x + 40
at x = 200,
C(200) = 0.25*200 + 40
= 50 + 40
= 90
Answer: 90

b)
C(x) = 0.25x + 40
at C(x) = 150,
150 = 0.25x + 40
0.25x = 110
x = 440
Answer: 440

c)
C(x) <=120
0.25x + 40 <= 120
0.25x <= 80
x <= 320
Answer: 320

d)
x can take all values from 0 to infinity
So, domain is:
[0, infinity)

e)
C(x) = 0.25x + 40
slope = d/dx(C(x)
= d/dx (0.25x + 40)
= 0.25

This means with every increase in mile, cost increases by $ 0.25

f)
C(x) = 0.25x + 40
for y intercept, put x=0
y intercept = 0.25*0 + 40
= 40