Respuesta :
Answer:
The number of units sold is 10.
Step-by-step explanation:
Given : The profit, in dollars, of a small business can be modeled by the function [tex]P(x) = 0.3x^2 + 7x-40[/tex], where x is the number of units sold.
To find : How many units need to be sold for the business to make a profit of $60?
Solution :
The profit, in dollars, of a small business can be modeled by the function [tex]P(x) = 0.3x^2 + 7x-40[/tex]
The profit is P(x)=60,
[tex]60 = 0.3x^2 + 7x-40[/tex]
[tex]0.3x^2 + 7x-100=0[/tex]
Using quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=0.3, b=7 and c=-100
[tex]x=\frac{-7\pm\sqrt{7^2-4(0.3)(-100)}}{2(0.3)}[/tex]
[tex]x=\frac{-7\pm\sqrt{169}}{0.6}[/tex]
[tex]x=\frac{-7\pm13}{0.6}[/tex]
[tex]x=\frac{-7+13}{0.6},\frac{-7-13}{0.6}[/tex]
[tex]x=10,-33.33[/tex]
Reject -33.33.
Therefore, the number of units sold is 10.
