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?
To find the linear function P, we'll use the slope-intercept form of a linear equation, which is given by:
P = ms + b
where P represents the profit, s represents the number of subscribers, m represents the slope, and b represents the y-intercept.
We are given two points (32,000, $98,000) and (35,000, $117,500) that lie on the line. Using these points, we can calculate the slope (m) and then substitute one of the points into the equation to find the y-intercept (b).
Step 1: Calculate the slope (m)
m = (y2 - y1) / (x2 - x1)
= ($117,500 - $98,000) / (35,000 - 32,000)
= $19,500 / 3,000
= $6.50
Step 2: Substitute one point into the equation to find the y-intercept (b)
Using the point (32,000, $98,000):
$98,000 = $6.50 * 32,000 + b
$98,000 = $208,000 + b
b = $98,000 - $208,000
b = -$110,000
Now, we can substitute the values of m and b back into the equation P = ms + b.
a.) The function P is given by:
P = $6.50 * s - $110,000
b.) To find the profit when the company has 50,000 subscribers:
P = $6.50 * 50,000 - $110,000
P = $325,000 - $110,000
P = $215,000
Therefore, the profit will be $215,000 if the company has 50,000 subscribers.
c.) To find the number of subscribers needed to break even, we need to determine when the profit (P) is equal to $0. Set P = 0 and solve for s:
0 = $6.50 * s - $110,000
$6.50 * s = $110,000
s = $110,000 / $6.50
s ≈ 16,923
Therefore, the company needs approximately 16,923 subscribers to break even.
you have two points (32000,98000) and (35000,117500)
Find the slope (117500-98000)/(35000-32000)
put into point slope form
y-y0=m(x-x0)
using one of the two points for x0 and y0.
b) Plug in x as 50,000 and solve for y.
c) plug in y as 0 and solve for x