Question

A car rental company charges a one-time application fee of 40 dollars, 55 dollars per day, and 13 cents per mile for its cars. A) Write a formula for the cost, C, of renting a car as a function of the number of days, d, and the number of miles driven, m. B) If C = f(d, m), then f(5, 600) =

Answer 1

Answer:

A) C = 40 + 55d + 0.13m

B) f(5,600) = $393

Step-by-step explanation:

First we need to convert all the units into dollars.

A car rental company charges:

an application fee of $40

$55 per day

13 cents = 13/100 = $0.13 per mile

A) The cost C of renting a car can be expressed as a function of number of days, d and the number of miles driven, m.

C = 40 + 55d + 0.13m

since $40 is a fixed cost which does not depend on time so we have added it as it is. The rest are added as a multiple of the parameter on which they depend i.e. days and miles.

B) C = f(d,m)

f(d,m) = 40 + 55d + 0.13m and we need to find f(5,600) i.e. here d = 5 and m = 600. So, we will substitute the values in the equation to find the total cost

f(5,600) = 40 + 55(5) + 0.13(600)

             = 40 + 275 + 78

f(5,600) = $393

Answer 2

Answer:

A) C(d,m) = 40 + 55d + 0.13m

B) $448

Step-by-step explanation:

Let 'd' be the number of days and 'm' the number of miles driven.

A) The cost function that describes a fixed amount of $40, added to a variable amount of $55 per day (55d) and a variable amount of 13 cents per mile (0.13m) is:

$C(d,m) = 40 +55d +0.13m$

B) If  d = 5 and m =600, the total cost is:

$C(5,600) = 40 +55*6 +0.13*600\\C(5,600)=\ 448$

The cost is $448.