Chapter 4.2, Problem 34E

(a)

To determine

To explain: the situation be modeled by a linear equation.

Answer to Problem 34E

There is a common difference between the values of x likewise values of y, the table above can be modeled by a linear equation.

Explanation of Solution

Given:

Consider the following table

Days	2	4	6	8
Total Cost (in Dollars)	246	450	654	858

Calculation:

For the table above to be modeled by a linear equation, there must be a common difference between every successive element in the values of x (days), likewise values of y (total cost)

Find the common difference between the values of x

Pick any two successive elements in the values of x and find the difference

Implies,

  $\begin{array}{l}\Delta x=4-2\hfill \\ =6-4\hfill \\ =2\hfill \end{array}$

Therefore, the common difference is, 2.

Find the common difference between the values of y

Pick any two successive elements in the values of y and find the difference

Implies,

  $\begin{array}{l}\Delta y=450–246\hfill \\ =654-450\hfill \\ =204\hfill \end{array}$

So, the common difference is, 204.

Since there is a common difference between the values of x likewise values of y, the table above can be modeled by a linear equation.

Conclusion:

Since there is a common difference between the values of x likewise values of y, the table above can be modeled by a linear equation.

(b)

To determine

To find: the processing fee and the daily fee.

Answer to Problem 34E

The equation is, $y=102x+42$ and the processing fee is, $42 and daily fee is $102.

Explanation of Solution

Calculation:

Use the linear equation $y=mx+c$ to model the table

Find the value of m

  $\begin{array}{l}m=\frac{\Delta y}{\Delta x}\\ =\frac{204}{2}\\ =102\end{array}$

Implies that,

  $y=102x+c$

To find the value of c , pick any paired elements $\left(x,y\right)$ from the table and substitute into

  $y=102x+c$

Put $x=4$ and $y=450$ into $y=102x+c$

Implies,

  $\begin{array}{l}450\text{ = }102\left(4\right)+c\hfill \\ c=42\hfill \end{array}$

Conclusion:

Therefore, the equation is, $y=102x+42$ and the processing fee is, $42 and daily fee is $102.

(c)

To determine

To find: the maximum number of days you can rent the beach house.

Answer to Problem 34E

The maximum number of days that the beach house can be rented with $1200 is, 11 days.

Explanation of Solution

Calculation:

Find the maximum number of days $1200can purchase.

This implies that, find x when $y=1200$

Hence,

  $\begin{array}{l}y=102x+42\hfill \\ 1200=102x+42\hfill \\ 102x=1158\hfill \\ x=11.4\hfill \end{array}$

Conclusion:

Therefore, the maximum number of days that the beach house can be rented with $1200 is, 11 days.