A blogger earns R(x)=2x+0.037x^2 in revenue, where x is the number of subscribers, and has a cost of C(x)=1650+3x.\
The blogger needs at least _ subscribers to break even.
To find the number of subscribers needed to break even, we need to set the revenue equal to the cost and solve for x.
So, R(x) = C(x).
2x + 0.037x^2 = 1650 + 3x.
Rearranging the equation, we get:
0.037x^2 + 2x - 3x - 1650 = 0.
Combining like terms:
0.037x^2 - x - 1650 = 0.
To solve this quadratic equation, we can either factor or use the quadratic formula. Since factoring may not always be feasible, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a.
For our equation, a = 0.037, b = -1, and c = -1650.
Substituting these values into the quadratic formula, we have:
x = (-(-1) ± √((-1)^2 - 4(0.037)(-1650))) / (2 * 0.037)
= (1 ± √(1 + 247.8)) / 0.074
= (1 ± √(248.8)) / 0.074.
Using a calculator to evaluate the equation, we find two solutions:
x ≈ 70.52 and x ≈ -45.52.
Since having negative subscribers does not make sense in this context, we can discard the negative solution.
The blogger needs at least 70.52 subscribers (rounded up to 71) to break even.