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.

Question

The blogger needs at least_ subscribers to break even

Answer 1

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.