Question

Eva needs to lease out a music studio to record her new album. The studio charges an hourly fee of $50 and an initial studio-use fee of $100. Make a table of values and then write an equation for P, commaP, in terms of t, commat, representing the amount of money Eva would have to pay to use the studio for tt hours.

Answer 1

To create a table of values and write the equation for the total cost \( P \) in terms of hours \( t \), let's analyze the costs involved:

1. Initial studio-use fee: $100
2. Hourly fee: $50/hour

The equation to represent the total cost \( P \) in terms of the number of hours \( t \) used can be expressed as:

\[
P = 50t + 100
\]

Here, \( 50t \) represents the cost for \( t \) hours of studio use, and the $100 is the initial fee.

### Table of Values

Now let's create a table of values for different hours \( t \):

| Hours \( t \) | Total Cost \( P \) |
|---------------|---------------------|
| 0 | \( P = 50(0) + 100 = 100 \) |
| 1 | \( P = 50(1) + 100 = 150 \) |
| 2 | \( P = 50(2) + 100 = 200 \) |
| 3 | \( P = 50(3) + 100 = 250 \) |
| 4 | \( P = 50(4) + 100 = 300 \) |
| 5 | \( P = 50(5) + 100 = 350 \) |

### Summary

The equation representing the amount of money Eva would have to pay to use the studio for \( t \) hours is:

\[
P = 50t + 100
\]

The table lists the total cost for using the studio from 0 to 5 hours.