SOLUTION: In the United States, the birthrate B for unmarried women (births per 1000 unmarried women) whose age is a is modelled by the function B(a) = −0.31x 2 + 16.54x 2 − 151.04

Algebra ->  Equations -> SOLUTION: In the United States, the birthrate B for unmarried women (births per 1000 unmarried women) whose age is a is modelled by the function B(a) = −0.31x 2 + 16.54x 2 − 151.04       Log On


   



Question 1197304: In the United States, the birthrate B for unmarried women (births per 1000 unmarried
women) whose age is a is modelled by the function
B(a) = −0.31x
2 + 16.54x
2 − 151.04
i. What is the age of unmarried women with the highest birthrate?
ii. What is the highest birthrate of unmarried women?
iii. Evaluate and interpret B(40).

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given function:
B(a) = −0.31x
2 + 16.54x
2 − 151.04
since this is not quite clear, I assume you have
B%28a%29+=+-0.31x%5E2+%2B+16.54x+-+151.04


i. What is the age of unmarried women with the highest birthrate?

if B%28a%29 is the birth rate then the value of "a" at B'%28a%29=0 will tell the age of unmarried women of highest+birth+rate.

B%28a%29+=+-0.31x%5E2+%2B+16.54x+-+151.04+
derivative is:
+B'%28a%29=-2%2A0.31x+%2B+16.54
+B'%28a%29=-0.62x+%2B+16.54
set it equal to zero
-0.62x+%2B+16.54=0
-0.62x+=-+16.54
x+=-+16.54%2F-0.62
x=26.677

or, you can find x-coordinate this way:
B%28a%29+=+-0.31x%5E2+%2B+16.54x+-+151.04+ =>a=-0.31, b=16.54,c=-151.04
x=-b%2F2a
x=-16.54%2F%282%2A%28-0.31%29%29
x=16.54%2F0.62
x=26.677+


ii. What is the highest birthrate of unmarried women?
if x=26.677, then

B%2826.677%29+=-0.31%2A26.677%5E2+%2B+16.54%2A26.677+-+151.04+
B%2826.677%29+=-220.61532199%2B+441.23758+-+151.04+
B%2826.677%29+=69.582

iii. Evaluate and interpret B%2840%29.

B%2840%29+=-0.31%2A40%5E2+%2B+16.54%2A40-+151.04+
B%2840%29+=-496+%2B+661.6-+151.04+
B%2840%29+=14.56