A blogger earns R(x)=8x+0.037x^2 in revenue, where x is the number of subscribers, and has a cost of C(x)=2400+3x.
The blogger needs at least_ subscribers to break even
To find the number of subscribers the blogger needs to break even, we need to set the revenue and cost equal to each other and solve for x:
R(x) = C(x)
8x + 0.037x^2 = 2400 + 3x
0.037x^2 + 5x - 2400 = 0
Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac))/(2a), where a = 0.037, b = 5, and c = -2400, we can determine the two possible values for x:
x = (-5 ± sqrt(5^2 - 4(0.037)(-2400)))/(2(0.037))
x = (-5 ± sqrt(25 + 355.2))/0.074
x = (-5 ± sqrt(380.2))/0.074
Using a calculator, we find that the two possible values for x are approximately x ≈ 41.342 and x ≈ -135.342.
Since the number of subscribers cannot be negative, the blogger needs at least approximately 41.342 subscribers to break even.