Question

Mohal needs to lease out a music studio to record his new album. The studio charges

an initial studio-use fee plus an hourly fee for each hour in the studio. Let P
represent the total amount of money Mohal would have to pay to use the studio for t
hours. The table below has select values showing the linear relationship between t
and P. Determine how much Mohal would need to pay in studio fees if he needed to
use the studio for 0.5 hours.

Answer 1

Mohal would need to pay $450 if he needed to use the studio for 0.5 hours.

Given the points (3, 700) and (7, 1100), the slope (m) is calculated as the change in P divided by the change in t:

m = (1100 - 700) / (7 - 3) = 400 / 4

= 100

Using the slope (m = 100) and one of the points (let's use 3, 700), we find the initial studio-use fee (b):

b = 700 - 100 * 3 = 700 - 300

= 400

The linear relationship is then expressed as:

P = 100t + 400

To find the cost for using the studio for 0.5 hours (t = 0.5):

P = 100 * 0.5 + 400 = 50 + 400

= 450