A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost
f
(
m
)
is a function of the number of miles
m
that the car is driven.
Plan A:
f
(
m
)
=
0.12
m
+
75
Plan B:
f
(
m
)
=
0.35
m
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
I. For Plan A, the total cost of the car rental is 75 dollars plus 12 cents for each mile driven. In other words, there is a flat fee of 75 dollars, and an additional charge of 12 cents per mile driven. For Plan B, the total cost of the car rental is 35 cents for each mile driven. This means that there is no flat fee but the cost per mile is higher at 35 cents per mile.
II. The rate of change for each function is the amount the total cost changes for each additional mile driven. For Plan A, the rate of change is 0.12 dollars or 12 cents. This means that for each mile driven, the total cost increases by 12 cents. For Plan B, the rate of change is 0.35 dollars or 35 cents, meaning that for each mile driven, the total cost increases by 35 cents.
III. To determine which plan is more cost-effective for a rental that will include a maximum of 250 miles, we need to calculate the total cost for both plans given 250 miles driven.
For Plan A:
f(m) = 0.12m + 75
f(250) = (0.12)(250) + 75 = 30 + 75 = 105 dollars
For Plan B:
f(m) = 0.35m
f(250) = (0.35)(250) = 87.5 dollars
Based on the calculations, Plan B is the most cost-effective for a car rental that will include a maximum of 250 miles driven, as the total cost is 87.5 dollars compared to 105 dollars for Plan A.