Chapter 4.2, Problem 34E

a.

To determine

If the given situation be modeled by a linear equation.

Answer to Problem 34E

Given situation can be modeled by a linear equation.

Explanation of Solution

Given Information: Data table of days and total cost is given.

Calculating the slope of consecutive points,

  $m=\frac{450-246}{4-2}=\frac{654-450}{6-4}=\frac{858-654}{8-6}=102$

As the slope is same in all cases,

so, given situation can be modeled by a linear equation.

b.

To determine

To find: The processing fee and the daily fee.

Answer to Problem 34E

Processing fee is $\$42$ and daily fee is $\$102$ .

Explanation of Solution

Given information: Data table of days spent $x$ and total cost $y$ is given.

Calculation:

Point slope formula: $y-y_1=m(x-x_1)$

  $m=102$(from previous part)

Considering the point $(2,246)$ ,

  $y-246=102(x-2)$

  $y=102x-204+246$ (Distributive property and rearranging)

  $y=102x+42$

When $x=0$,

  $y=42$

  $y-\mathrm{int}ercept$ symbolizes processing fee,

Processing fee: $\$42$

Daily fee: $\frac{246-42}{2}=\$102$

Thus, processing fee is $\$42$ and daily fee is $\$102$ .

c.

To determine

To find: The maximum number of days one can spend on beach with a budget of $\$1200$ .

Answer to Problem 34E

Maximum $11$ days can be spent at beach in given budget.

Explanation of Solution

Given information: Data table of days spent $x$ and total cost $y$ is given, $y=102x+42$ (from previous part).

Calculation:

Putting $y=1200$ in equation $y=102x+42$ ,

  $\begin{array}{l}1200=102x+42\\ 102x=1200-42\\ 102x=1158\\ x=\frac{1158}{102}\\ x\approx 11.35\end{array}$

As days cannot be in fraction, $\therefore$ maximum $11$ days can be spent at beach in given budget.