Question

An online music service that sells song downloads models it's profit using the function P(d)=-5d^2+450d-1000, where d is the number of downloads sold and P is the profit. How many downloads does it need to sell to make a profit of more than $8000?

Answer 1

Answer:

Step-by-step explanation:

P(d) ≥ 8000

P(d) = - 5d^2 + 450d - 1000 ≥ 8000 Subtract 8000 from both sides

-5d^2 + 450d - 1000 - 8000 ≥ 0          Combine like terms

-5d^2 + 450d - 9000 ≥ 0                      Divide through by - 5

d^2 - 90d + 1800 ≥ 0                             Factor

(d - 60)(d - 30)

So d ≥ 60

or d ≥ 30

So if customers make more than 30 downloads, the profit goes up 8000.