The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t^4 – 9t^3 + 24t^2 – 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

(2 months isn’t the answer btw)

The profitability of the restaurant is when the function gives a value greater than 0. The franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Given that:

To calculate the profit, we simply substitute the values of t in the above equation.

(a) 5 months

This means

So, we have:

(b) 3 months

This means that

So, we have:

(c) 2 months

This means that

So, we have:

(d) 1 month

This means that

So, we have:

For the restaurant to make a profit, the equation has to give a positive value. Since none of the values of t gives a positive value for P(t).

Then, we can say the franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Read more about functions at:

true !

step-by-step explanation: