<u><em>Answer:</em></u>The youngest age was 26.1843 years
<u><em>Explanation:</em></u><u>The equation that models the average income is:</u>
i = -425x² + 45500x - 650000
where:
i is the average income
x is the age
We are looking for the age at which the income was $250000.
<u>Therefore, we will substitute with i = 250000 in the above equation and solve for x as follows:</u>
250000 = -425x² + 45500x - 650000
425x² - 45500x + 650000 + 250000 = 0
425x² - 45500x + 900000 = 0
<u>The general form of the quadratic equation is:</u>
ax² + bx + c = 0
<u>By comparison:</u>
a = 425
b = -45500
c = 900000
<u>Substitute in the quadratic formula shown in the attached image to get the values of x.</u>
<u>We will find that:</u>
either x = 80.8744
or x = 26.1843
Since we are looking for
the younger age, therefore, our answer would be:
26.1843 years
Hope this helps :)