Chapter 4.3, Problem 15Q

a.

To determine

To write: A linear model that represents the total cost as a function of number of months website is maintained.

Answer to Problem 15Q

  $\text{The linear model is }y=44x+48$.

Explanation of Solution

Given Information: Initial fees is $\text{\$48}$ , thereafter maintenance fee is $\text{\$44}$ per month.

Calculation:

As per given information points are $(0,48)$ and $(1,92)$ ,

Slope-intercept form: $y=mx+b$

Where $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{92-48}{1-0}\\ m=44\end{array}$

When $x=0$ , $y=48$

  $\therefore y-\mathrm{intercept}(b)=48$

Substituting the values in slope-intercept form,

  $y=44x+48$

  $\text{Thus, the linear model is }y=44x+48.$

b.

To determine

To find: The total cost of setting up a website and maintaining it for six months.

Answer to Problem 15Q

The cost will be $\$312$ .

Explanation of Solution

Given information: Initial fees is $\text{\$48}$ , thereafter maintenance fee is $\text{\$44}$ per month. Linear model from previous part.

Calculation:

  $y=44x+48$

Putting $x=6$ in above equation,

  $\begin{array}{l}y=44(6)+48\\ y=312\end{array}$

Thus, the cost will be $\$312$ .

c.

To determine

To find: The company in which website can be set up and maintained for greatest amount of time.

Answer to Problem 15Q

The company that charges an initial fees of $\$48$ would be preferable, as it sets up and maintains the website for $13\mathrm{months}$ at $\$620$ .

Explanation of Solution

Given information: Initial fees is $\$0$ , thereafter maintenance fee is $\$62$ per month. Linear model from one of the previous parts.

Calculation:

For the second company points are $(0,0)$ and $(1,62)$ ,

  $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{62-0}{1-0}\\ m=62\end{array}$

  $y-\text{intercept(b)}=0$

  $(whenx=0)$

Substituting values in slope-intercept form,

  $y=62x$

Putting $y=620$ ,

  $x=10\mathrm{months}$

First company’s equation: $y=44x+48$

Putting $y=620$ ,

  $\begin{array}{l}620=44x+48\\ 44x=572\\ x=13months\end{array}$

Thus, the company that charges an initial fees of $\$48$ would be preferable, as it sets up and maintains the website for $13\mathrm{months}$ at $\$620$ .