Question

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)=-0.355a^2+19.17a-213.37.
a) what is the age of unmarried women with the highest birth rate?
b)what is the highest birth rate of unmarried women?

Answer 1

Using the given function we calculate the highest birth-rate for unmarried women is at the age of (a)27 years and the rate is (b) 45.425 .

a) The function that represents the above social situation is given by :

B(a)=-0.355a²+19.17a-213.37. where a is the age.

Now this is a quadratic function.

To find the maximum value of the function we have to find the first derivative of the function.

B(a)=-0.355a²+19.17a-213.37

or, B'(a) = -0.71a + 19.17

Now at B'(a) = 0 , we find the value of a for which the rate is maximum.

∴ -0.71a + 19.17 = 0

or, a = 19.17 / 0.71

or, a = 27 years

b) Now we will find the highest birthrate for a = 27

∴ B(27) = -0.355(27)²+19.17(27)-213.37

or,  B(27) = 45.425

Hence the highest birthrate is 45.425 per 100 unmarried women.

A function is a relationship between a single set of inputs and outputs. Simply described, a function is a relationship between inputs in which each input is coupled with exactly one output. There is a range, codomain, and domain for every function.

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