Question

The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:

What is the youngest age for which the average income of a lawyer is $450,000?

Round to the nearest year.

Answer 1

The answer is 37 years old.

I = -425x² + 45500x -650000
I = 450000

-425x² + 45500x -650000 = 450000
-425x² + 45500x - 650000 - 450000 = 0
-425x² + 45500x - 1100000 = 0

Divide all factors by 25:
- 17x² + 1820x - 44000 = 0

This is quadratic equation (ax² + bx + c = 0)
$x_{1,2} = \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} = \frac{-1820+/- \sqrt{ 1820^{2}-4*(-17)*(-44000) } }{2*(-17)} = \\ \\ = \frac{-1820+/- \sqrt{3312400-2992000 } }{-34} = \frac{-1820+/- \sqrt{320400} }{-34} =\frac{-1820+/- 566}{-34} \\ \\ x_1= \frac{-1820+ 566}{-34}= -37 \\ \\ x_2 = \frac{-1820- 566}{-34}=70$

Since, the youngest age is needed, the correct answer is x = 37