Question

A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $75 per hour. a. Write a linear model that represents the total cost C of recording an album as a function of studio time (in hours). Use the variable t to represent the number of hours the recording studio is used. B. Is it less expensive to purchase 12 hours of recording time at the studio or a $750 music software program that you can use to record on your own computer? Explain your reasoning. The cost for 12 hours of recording time is $

Answer 1

`\begin{gathered} a)\text{ C = 75t + 50} \\ \\ b)\text{ The \$750 music software program is better} \end{gathered}`

a) Here, we want to write an equation representing the total cost in relation to the number of hours

The total cost is to be represented by C while the number of hours is to be represented by t

The total cost is the dependent variable (y-value) while the number of hours t is the independent variable (x-value)

So, the linear model with respect to the above will be;

`C\text{ = 75t + 50}`

b) Here, we want to compare costs

To do this, we need to get the cost of 12 hours of recording

What we simply need to do here is to substitute the value of 12 for t in our linear model

Mathematically, that would be;

`\begin{gathered} C\text{ = 75(12) + 50} \\ \\ C\text{ = \$950} \end{gathered}`

Looking at the costs, we can see that purchasing the software is a better option since it costs less