Chapter 2.4, Problem 48AYU

(a)

To determine

To find: the fee for parking in the short term parking garage for 2 hours.

Answer to Problem 48AYU

The parking fee for 3 hours is $3.

Explanation of Solution

Given information:

The short term parking fee $F$ for parking $x$ hours at $O$ ’s H International airport’s main parking garage can be modeled by the function

  $F\left(x\right)=\{\begin{array}{l}3\text{\hspace{1em}if}0<x\le 3\\ 5\mathrm{int}\left(x+1\right)+1\text{\hspace{1em}if}3<x<9\\ 50\text{\hspace{1em}if}9\le x\le 24\end{array}$

Calculation:

We nota that when $x$ is hours is 2, the equation for $f$ is given by $F\left(x\right)=3$ .

Substitute $-1$ for $x$ in the function $F\left(x\right)$ and evaluate.

  $F\left(3\right)=3$

Thus, the parking fee for 3 hours is $3.

(b)

To determine

To find: the fee for parking in the short term parking garage for 7 hours.

Answer to Problem 48AYU

The parking fee for 7 hours is $41.

Explanation of Solution

Given information:

The short term parking fee $F$ for parking $x$ hours at $O$ ’s H International airport’s main parking garage can be modeled by the function

  $F\left(x\right)=\{\begin{array}{l}3\text{\hspace{1em}if}0<x\le 3\\ 5\mathrm{int}\left(x+1\right)+1\text{\hspace{1em}if}3<x<9\\ 50\text{\hspace{1em}if}9\le x\le 24\end{array}$

Calculation:

We nota that when $x$ is hours is 7, the equation for $f$ is given by $F\left(x\right)=5\mathrm{int}\left(x+1\right)+1$ .

Evaluate,

Replace $x$ with 7 in the above function and evaluate.

  $\begin{array}{c}F\left(7\right)=5\mathrm{int}\left(7+1\right)+1\\ =5\mathrm{int}8+1\\ =5\cdot 8+1\\ =41\end{array}$

Thus, the parking fee for 7 hours is $41.

(c)

To determine

To find: the fee for parking in the short term parking garage for 15 hours.

Answer to Problem 48AYU

The parking fee for 15 hours is $50.

Explanation of Solution

Given information:

The short term parking fee $F$ for parking $x$ hours at $O$ ’s H International airport’s main parking garage can be modeled by the function

  $F\left(x\right)=\{\begin{array}{l}3\text{\hspace{1em}if}0<x\le 3\\ 5\mathrm{int}\left(x+1\right)+1\text{\hspace{1em}if}3<x<9\\ 50\text{\hspace{1em}if}9\le x\le 24\end{array}$

Calculation:

We nota that when $x$ is hours is 15, the equation for $f$ is given by $F\left(x\right)=50$ .

Evaluate,

  $F\left(15\right)=50$

Thus, the parking fee for 15 hours is $50.

(d)

To determine

To find: the fee for parking in the short term parking garage for 8 hours and 24 minutes.

Answer to Problem 48AYU

The parking fee for 8 hours and 24 minutes is $46.

Explanation of Solution

Given information:

The short term parking fee $F$ for parking $x$ hours at $O$ ’s H International airport’s main parking garage can be modeled by the function

  $F\left(x\right)=\{\begin{array}{l}3\text{\hspace{1em}if}0<x\le 3\\ 5\mathrm{int}\left(x+1\right)+1\text{\hspace{1em}if}3<x<9\\ 50\text{\hspace{1em}if}9\le x\le 24\end{array}$

Calculation:

In order to find the parking fee for a period of 8 hours and 24 minutes or 8.4 hours, replace $x$ with 8.4 in the function $F\left(x\right)=5\mathrm{int}\left(x+1\right)+1$ and evaluate.

  $\begin{array}{c}F\left(8.4\right)=5\mathrm{int}\left(8.4+1\right)+1\\ =5\mathrm{int}9.4+1\\ =5\cdot 9+1\\ =46\end{array}$

Therefore, the parking fee for 8 hours and 24 minutes is $46.