We are given
The average income, I, in dollars is
[tex]I=-425x^2+45500x-650000[/tex]
(a)
now, we are given
average income is $275000
so, [tex]I=275000[/tex]
now, we can set them equal
and then we can solve for x
[tex]275000=-425x^2+45500x-650000[/tex]
[tex]-425x^2+45500x-925000=0[/tex]
we will have to use quadratic formula
[tex]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}[/tex]
[tex]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}[/tex]
we get
[tex]x=27.28199[/tex]
[tex]x=79.776[/tex]
we need to find youngest age
It means that we need to choose smallest value
so,
[tex]x=27[/tex]............Answer
(b)
we are given
x=40
so, we can plug it and find I
[tex]I=-425(40)^2+45500(40)-650000[/tex]
[tex]I=490000[/tex]..............Answer
