Question

Plessse help, thanks
The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 9t3 + 24t2 – 20t, where t is the number of months since the restaurant opened. How many months after the franchise opens will it begin to show a profit?

5 months
3 months
2 months
1 month

Answer 1

Replace t with the months given as choices to see which one gives a positive value as an answer.

P(1) = 1^4-9(1)^3 + 24(1)^2-20(1) = -4

P(2) = 2^4-9(2)^3+24(2)^2-20(2) = 0

P(3) = 3^4 -9(3)^3+24(3)^2-20(3) = -6

P(5) = 5^4-9(5)^3+24(5)^2-20(5) = 0

P(6) = 6^4-9(6)^3+24(6)^2-20(6) = 96

It shows a profit in month 6 so it would start showing a profit in month 5.

The answer is 5 months