Question

94. Birth Rate of Unmarried Women In the United States, the birth rate B of unmarried women (births per 1000 unmarried women) for women whose age is a is modeled by the function B(a) = -0.33a + 19.17a-213.37. (a) What is the age of unmarried women with the highest birth rate? 29.0 years (b) What is the highest birth rate of unmarried women? (e) Evaluate and interpret B(40).

Answer 1

Using concepts of quadratic equation, we have that:

a) The age of unmarried women with the highest birth rate 29 years.

b) The highest birth rate of unmarried women is of 65 births per 1000 unmarried women.

c) B(40) = 25.43, which means that the birth rate of unmarried women of age 40 is of 25.43 births per 1000 unmarried women.

The birth-rate for women of age a is given by:

$B(a) = -0.33a^2 + 19.17a - 213.37$

Which is a quadratic equation with coefficients $a = -0.33, b = 19.17, c = -213.37$

Item a:

The age with the highest value is the a-value for the vertex, which is:

$a_V = -\frac{b}{2a} = -\frac{19.17}{2(-0.33)} = 29$

The age of unmarried women with the highest birth rate 29 years.

Item b:

The rate is B(29), which is:

$B(29) = -0.33(29)^2 + 19.17(29) - 213.37 = 65$

The highest birth rate of unmarried women is of 65 births per 1000 unmarried women.

Item c:

$B(40) = -0.33(40)^2 + 19.17(40) - 213.37 = 25.43$

B(40) = 25.43, which means that the birth rate of unmarried women of age 40 is of 25.43 births per 1000 unmarried women.

A similar problem is given at brainly.com/question/24626341