Question

maya needs to lease out a music studio to record her new album. the studio charges an initial studio - use fee plus an hourly fee for each hour in the studio. the total amount of money maya will have to pay to use the studio for t hours can be determined using the equation p = 50t + 100. what is the y - intercept of the equation and what is its interpretation in the context of the problem?
the y - intercept of the function is (square) which represents
the total number of hours maya used the studio
the initial fee of using the studio
the additional price per hour of using the studio
the total price of using the studio for the day

Explanation:

Step1: Recall linear function form

A linear function is in the form \( P = mt + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value when \( t = 0 \)).

Step2: Identify y - intercept in given equation

The given equation is \( P = 50t+100 \). Comparing with \( P = mt + b \), we see that \( b = 100 \).

Step3: Interpret the y - intercept

When \( t = 0 \) (number of hours used is 0, i.e., at the start), \( P=100 \). This represents the initial fee to use the studio because it's the cost when no hours have been used yet.

Answer:

The y - intercept of the function is \( 100 \), which represents the initial fee of using the studio.