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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