The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 10t3 + 28t2 – 24t, 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? A. 0 months
B. 2 months
C. 4 months
D. 6 months

In this question, the profit of the restaurant after t months is given by a polynomial function. To find when it begins to show a profit, we find the numerical values of the function for t, and it shows a profit when

Profit after t months:

0 months:

This is P(0). So

1 month:

This is P(1). So

2 months:

This is P(2). So

3 months:

This is P(3). So

4 months:

This is P(4). So

5 months:

This is P(5). So

6 months:

This is P(6). So

7 months:

This is `P(7). So

After 7 months it shows profit, so it starts showing profit on the 6th month, and thus, the correct answer is given by option D.

For another example of a function involving numeric value, you can check

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