4.6 = 0.0014 x^2 − 0.1529 x + 5.855?
According to a survey conducted in 1990 by
Independent Sector, the percent of their incomes that Americans give to charities is related to their household incomes. For families with annual incomes between $5000 and
$100,000, the percent is modeled by
P = 0.0014x^2−0.1529x+5.855
Where P is the percentage of annual income
given and x is the annual income in thousands
of dollars.
What is the largest of the two annual incomes at which Americans give 4.6%(P =
4.6) of their income to charity?
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4.6 = 0.0014 x^2 − 0.1529 x + 5.855
0.0014 x^2 − 0.1529 x + 1.255 = 0 => multiply by 10,000
14x^2 - 1529x + 12550 = 0
using the quadratic formula:
ax² + bx + c = 0
x = [– b ± √(b² – 4ac)] / 2a
in this case: a = 14 , b = -1529 , c = 12550
plug in for a, b & c and solve:
x = [1529 ± √(2337841 – 702800)] / 28
x = [1529 ± √(1635041)] / 28
x ≈ 8.94 , 100.28
Answer => 100.28