Chapter 1.3, Problem 95E

(a)

To determine

Function of the cost C of parking in a metered lot for t hours.

Answer to Problem 95E

The function is $C(t)=1+0.50[t-1]$

Explanation of Solution

Given data:

The cost parking in a metered parking lot is $1.00 for first hour.

Additional charges are $0.50

Formula used:

Least integer function:

  $F(x)=\{\begin{array}{l}0<x\le 1x=1\\ 1<x\le 2x=2\\ 2<x\le 3x=3\end{array}$

Calculation:

The Function of the cost C of parking in a metered lot for t hours:

As the cost for first parking is $1.00 and as additional charges are $0.50

And charges are adding with the increasing time of parking. So the equation is:

  $C(t)=1+0.50[t-1]$

Conclusion:

The function is $C(t)=1+0.50[t-1]$

(b)

To determine

To calculate: Cost of parking for 7 hours and 10 minutes

Answer to Problem 95E

The cost of parking for 7 hours and 10 minutes is $4.50

Explanation of Solution

Given information:

  $C(t)=1+0.50[t-1]$

Calculation:

The graph for the function is:

X	-2	-1	0	1	2	3
Y	-0.5	0	0.5	1	1.5	2

  

The cost of parking for 7 hours and 10 minutes ( $\frac{7}{6}\text{hours}=7.16\text{hours}$ )

  $\begin{array}{l}C(t)=1+0.50[t-1]\\ C(\frac{7}{6})=1+0.50[7.16-1]\\ C(\frac{7}{6})=1+0.50[6.16]\\ C(\frac{7}{6})=1+0.50(7)\\ C(\frac{7}{6})=4.5\$\end{array}$

Conclusion:

The cost of parking for 7 hours and 10 minutes is $4.50