Chapter 2.4, Problem 9E

a.

To determine

To sketch:the graph of the cost of parking at this lot as a function of the time parked there.

Explanation of Solution

Given:

The charge of parking lot for the first hour is $\$3$ .

And the charge extends (after 1 hour) per hour is $\$2$ up to maximum daily limit is $\$10$ .

Calculation:

As the charge of parking lot for the first hour is $\$3$ .

Therefore, the charge of parking lot for the next hour at the rate of $\$2$ is as follows:

  $\begin{array}{l}2\text{nd}\text{hrs}=\$3+\$2=\$5\\ \text{3rd}\text{hrs}=\$5+\$2=\$7\\ \text{4th}\text{hrs}=\$7+\$2=\$9\\ \text{5th}\text{hrs}=\$9+\$2=\$11\end{array}$

According to the question, the maximum daily limit is $\$10$ .

Therefore, the charges for 5^th hrs is $\$10$ instead of $\$11$ .

Now, the graph of the cost of parking at this lot as a function of the time parked:

Let yas a function of the time parked.

The graph is shown below:

  

b.

To determine

To discuss: the discontinuity of the function and their significance.

Answer to Problem 9E

A step graphs.

Explanation of Solution

Given:

The charge of parking lot for the first hour is $\$3$ .

And the charge extends (after 1 hour) per hour is $\$2$ up to maximum daily limit is $\$10$ .

Calculation:

The charge of parking from part (a) is as follows:

  $1\text{st}\text{hrs}=\$3,2\text{nd}\text{hrs}=\$5,\text{3rd}\text{hrs}=\$7,\text{4th}\text{hrs}=\$9,\text{5th}\text{hrs}=\$10,6\text{th}\text{hrs and next}\text{hrs}=\$10$

The graph is a step graph. It is significant for those who park there to be aware of the time they have spent parked. If they exceed their hour even slightly, they will be charged for an entire hour longer.

The discontinuities occur at every hour until the 6th where the graph is then continuous to the right from 10 dollars onward.

Hence, the above graph is step graph.