Chapter 4.1, Problem 30E

(a)

To determine

To find: the total cost of recording an album as a function of studio time.

Answer to Problem 30E

The linear model is $y=75x+50$ .

Explanation of Solution

Given:

Consider an initial fee of $50 and an additional fee of $75 per hour.

Calculation:

Let x be the number of hours and y be the total cost.

Therefore, the linear equation that models the situation is

  $y=75x+50$

So, the linear model is

  $y=75x+50$

Conclusion:

Therefore, the linear model is $y=75x+50$ .

(b)

To determine

To explain: it is more expensive or less expensive to purchase 12 hours than a $750 music software program.

Answer to Problem 30E

Therefore, it is more expensive to purchase 12 hours than a $750 music software program.

Explanation of Solution

Given:

Consider an initial fee of $50 and an additional fee of $75 per hour.

Calculation:

Put $x=\text{1}2$ , then

  $\begin{array}{l}y=75\left(12\right)+50\hfill \\ =950\hfill \end{array}$

Thus, one will spend $950 for 12 hours.

Conclusion:

Therefore, it is more expensive to purchase 12 hours than a $750 music software program.