The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 10t3 + 28t2 – 24t, where t i
s 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.
Explanation: Find the greatest common factor for all of them. Which is 6. Then you just divide each number by 6 48/6= 8 30/6= 5 42/6= 7 Making it 8:5:7