Final answer:
The linear model for the total cost of recording an album in terms of studio time used is represented by the equation C = 50 + 75t, where $50 is the initial fee and $75 is the hourly rate.
Step-by-step explanation:
The subject of this question is to create a linear model that represents the total cost of recording an album as a function of the studio time used. The recording studio in question charges an initial fee plus an hourly rate for studio time. Using the provided information, we can write the linear model for the total cost, C, in terms of the studio time, t in hours, as follows:
C = 50 + 75t
In this equation, $50 represents the initial fee that is charged regardless of the number of hours used, which is a fixed cost. The $75 represents the hourly rate charged for each hour of studio time, which is a variable cost. As the number of hours, t, increases, the total cost, C, increases linearly with the equation reflecting that directly proportional relationship.