Question

The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function: I = -425x^2 + 45,500x – 650,000.
What is the youngest age for which the average income of a lawyer is $275,000? Round to the nearest year.

According to this model, what is the predicted average annual income of 40-year-old lawyers? Round to the nearest whole dollar.

Answer 1

We are given

The average income, I, in dollars is

$I=-425x^2+45500x-650000$

(a)

now, we are given

average income is $275000

so, $I=275000$

now, we can set them equal

and then we can solve for x

$275000=-425x^2+45500x-650000$

$-425x^2+45500x-925000=0$

we will have to use quadratic formula

$x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}$

$x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}$

we get

$x=27.28199$

$x=79.776$

we need to find youngest age

It means that we need to choose smallest value

so,

$x=27$............Answer

(b)

we are given

x=40

so, we can plug it and find I

$I=-425(40)^2+45500(40)-650000$

$I=490000$..............Answer