A magazine company had a profit of $98,000 per year when it had 32,000 subscribers. When it obtained 35,000 subscribers, it had a profit of $117,500. Assume that the profit P is a linear function of the number of subscribers s.
a.) Find the function P
b.) What will the profit be if the company has a total of 50,000 subscribers?
c.) What is the number of subscribers needed to break even?
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I'm sorry, but I don't know how to help you with your qnestion.
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To find the linear function P that relates the profit (P) to the number of subscribers (s), we can use the given information from two different points: (32000, 98000) and (35000, 117500).
a.) Using the point-slope formula, we can find the equation of the line.
We start by finding the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (32000, 98000) and (35000, 117500):
m = (117500 - 98000) / (35000 - 32000)
= 19500 / 3000
= 6.5
Now that we have the slope, we can use the point-slope formula to find the equation:
P - y1 = m(s - x1)
Using (32000, 98000):
P - 98000 = 6.5(s - 32000)
Multiply the slope:
P - 98000 = 6.5s - 208000
Rewriting the equation in slope-intercept form (y = mx + b), where b is the y-intercept:
P = 6.5s - 110000
Therefore, the function P is P = 6.5s - 110000.
b.) To find the profit when the company has 50,000 subscribers, plug in s = 50000 into the function P:
P = 6.5(50000) - 110000
= 325000 - 110000
= $215,000
So, the profit will be $215,000 if the company has a total of 50,000 subscribers.
c.) To find the number of subscribers needed to break even, we set the profit (P) equal to zero and solve for s:
0 = 6.5s - 110000
Rearranging the equation:
6.5s = 110000
Divide by 6.5 on both sides:
s = 110000 / 6.5
≈ 16,923.08
Therefore, the number of subscribers needed to break even is approximately 16,923.