Question

the average annual income, /, in dollars, of a lawyer with an age of x years is modeled with 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 $250,000?

Answer 1

26 years of age.

Explanation:

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

I = - 425x² + 45500x - 650000 .......... (1)

If the average annual income of the lawyer at the age of x years is $250000, then from the equation (1) we can write

- 425x² + 45500x - 650000 = 250000

⇒ - 425x² + 45500x - 900000 = 0

⇒ - 17x² + 1820x - 36000 = 0

Now, using the quadratic formula,

`x = \frac{- 1820 \pm \sqrt{(1820)^(2) - 4(-17)(- 36000) } }{2(- 17)} = (-1820 + 929.73)/(- 34) = 26` years (Approximate)

{We have neglected the other root as we need the youngest age}(Answer)