An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be give
n by the function P(x) = x3 – 4x2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)?
To determine the number of years when the company will breakeven, we use the equation given. At the breakeven point, the company has no profit and loses. So, we P(x) = 0. We calculate as follows: <span>P(x) = x3 – 4x2 + 3x – 12 0 = </span>x^3 – 4x^2 + 3x – 12 x = 4 , 1.732i, -1.732i
Solving for x, we will have three value one real and 2 imaginary values. Since time cannot be negative and imaginary. The answer would be 4. After 4 years, the company will break even.
Both answers are not the same. You are correct and your friend is wrong. The situation your teacher gave could have only one other interpretation that would be acceptable and that would be 8t+3 because it is the same number just in a different order.
