Question

6. A profit function for a new business follows the functionP(x) = 1/3x^2 - 6x, where x represents the number of months.After how many months will the company begin to make aprofit?A. 2B. 9C. 12D. 18

Answer 1

It will take 18 months before the company starts making a profit.

Explanation

Given information

`P(x)\text{ = }(1)/(3)x^2\text{ - 6x}`

Where x is the number of months.

Step 1: Make P(x) = 0

`\begin{gathered} \text{ p(x) = }(1)/(3)x^2\text{ - 6}x \\ 0\text{ = }(1)/(3)x^2\text{ - 6}x \end{gathered}`

Step 2: Find x from the above equation

`\begin{gathered} 0\text{ = }(1)/(3)x^2\text{ - 6x} \\ \text{Add 6x to the both sides} \\ 0\text{ + 6x = }(1)/(3)x^2\text{ - 6x + 6x} \\ 6x\text{ = }(1)/(3)x^2 \\ \text{cross multiply} \\ 6x\text{ }*3=x^2 \\ 18x=x^2 \\ \text{Divide both sides by x} \\ \frac{18\cancel{x}}{\cancel{x}}\text{ = }\frac{\cancel{x^2}}{\cancel{x}} \\ x\text{ = 18 months} \end{gathered}`

Therefore, it will take 18 months before the company starts making a profit.