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.

$C=$

Question 2
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?
It is less expensive to purchase

Answer 1

The linear model that represents the total cost C of recording an album as a function of studio time (in hours) is C = 50 + 75t. It is less expensive to purchase a $750 music software program than to purchase 12 hours of recording time at the studio.

Step-by-step explanation:

The linear model that represents the total cost C of recording an album as a function of studio time (in hours) can be written as:

C = 50 + 75t

This equation represents the initial fee of $50 plus $75 per hour of studio time. So, the total cost of recording an album is the sum of the initial fee and the product of the studio time and the hourly rate.

To determine whether it is less expensive to purchase 12 hours of recording time at the studio or a $750 music software program, we can substitute the value of t in the equation with 12 and calculate the total cost.

C = 50 + 75(12) = 50 + 900 = $950

The total cost of purchasing 12 hours of recording time at the studio is $950.

Now, we can compare this with the cost of the $750 music software program. Since $950 is greater than $750, it is less expensive to purchase the music software program.