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Evgesh-ka [11]
3 years ago
7

Carson needs to lease out a music studio to record his new album. The studio charges an initial studio-use fee plus an hourly fe

e for each hour in the studio. The total amount of money Carson would have to pay to use the studio for tt hours can be determined using the equation P=50t+100.P=50t+100. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?
Mathematics
1 answer:
Naily [24]3 years ago
5 0

Answer:

The y-intercept of the equation is 100 and represents the initial studio-use fee.

Step-by-step explanation:

In this equation, our t variable (time) is the equivalent of the x-variable on a graph. This is because it is the variable that we 'change' to see its impact on y. We see how the amount of hours affects the price. So our P variable (price) is the equivalent of y on a graph. The y-intercept is where the line crosses the y-axis on a graph. At this point, x=0.

Since P is our y, and t is our x, to find the y-intercept, we simply need to make t = 0.

P = 50(0) + 100

P = 100

Therefore the y-intercept is 100.

In this context, t represents time, so even though the studio has been used for 0 hours, the price is still 100. This is because the 100 represents the initial studio-use fee, and using it for certain amounts of time adds onto the initial fee of $100. The hourly fee is represented by 50t so it costs $50 more for each hour of use.

Hope this helped!

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