Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.
What is a quadratic function?
A quadratic function is given according to the following rule:
y = ax² + bx + c
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation that models the income as function of age is given by:
I(x) = -425x² + 45500x - 650000.
The income is of 250,000 when I(x) = 250000, hence:
250000 = -425x² + 45500x - 650000.
425x² - 45500x + 900000 = 0.
Hence the coefficients are a = 425, b = -45500 and c = 900000, then:
- [tex]\Delta = (-45500)^2 - 4(425)(900000) = 540250000[/tex]
- [tex]x_1 = \frac{45500 + \sqrt{540250000}}{2(425)} = 80.87[/tex]
- [tex]x_2 = \frac{45500 - \sqrt{540250000}}{2(425)} = 26.18[/tex]
The youngest age for which the average income of the lawyer is of $250,000 is of 26 years. (the oldest is of 81 years).
More can be learned about quadratic equations at https://brainly.com/question/24737967
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