Chapter 2.4, Problem 54AYU

Car Rental Costs An economy car rented in Florida from Enterprise® on a weekly basis costs $\$185$ per week. Extra days cost $\$37$ per day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Also, any part of a day used counts as a full day. Find the cost $C$ of renting an economy car as a function of the number $x$ of days used, where $7\le x\le 14$. Graph this function.

To determine

To find:

a. The cost $C$ of renting an economy car as a function of number $x$ of days used, where $7 \le x \le 14$.

Answer to Problem 54AYU

Solution:

a.

$C\left(x\right)=\{\begin{array}{l}185if x=7\\ 222 if 7<x\le 8\\ 259 if 8<x\le 9\\ 296 if 9<x\le 10\\ 333 if 10<x\le 11\\ 370 if 11<x\le 14\end{array}$

Explanation of Solution

Given:

IIt is given that an economy car rented in Florida from Enterprise on a weekly basis costs $\$185$ per week.

Extra days cost $\$37$ per day until the day rate exceeds the weekly rate, in which case the weekly rate applies.

Part of a day used counts as a full day.

$37 \times 5 = 185$

In a week, from 5^th day the cost becomes weekly basis as 5^th day itself cost 185.

a. Let the function for the cost be $C\left(x\right)$ The function can be defined as

$C\left(x\right)=\{\begin{array}{l}185if x=7\\ 222 if 7<x\le 8\\ 259 if 8<x\le 9\\ 296 if 9<x\le 10\\ 333 if 10<x\le 11\\ 370 if 11<x\le 14\end{array}$

To determine

To find:

b. Graph the function from part a).

Answer to Problem 54AYU

Solution:

b.

Explanation of Solution

Given:

IIt is given that an economy car rented in Florida from Enterprise on a weekly basis costs $\$185$ per week.

Extra days cost $\$37$ per day until the day rate exceeds the weekly rate, in which case the weekly rate applies.

Part of a day used counts as a full day.

$37 \times 5 = 185$

In a week, from 5th day the cost becomes weekly basis as 5th day itself cost 185.

b.