Question

the following table shows the births per thousand individuals for human females of various ages in 2011
age in years
12
17
22
27
32
37
42
births per 1000
0.6
42.5
106.4
117.6
99.9
47.5
9.5
to the nearest hundredth, how many births per 1000 are there for women who are 30 years old?

Explanation:

Step1: Identify the age group

The age we are interested in is 30 years old. Looking at the age column, we need to find the value corresponding to 30. But the given ages are 12,17,22,27,32,37,42. 30 is not in the list. We can assume this is a linear - interpolation problem. The two closest ages are 27 and 32.

Step2: Set up the linear - interpolation formula

The linear - interpolation formula is \(y = y_1+\frac{(y_2 - y_1)}{(x_2 - x_1)}(x - x_1)\), where \(x\) is the target age (30), \(x_1 = 27\), \(x_2=32\), \(y_1 = 117.6\) (births per 1000 for age 27), \(y_2 = 99.9\) (births per 1000 for age 32).
First, calculate the slope \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{99.9 - 117.6}{32 - 27}=\frac{- 17.7}{5}=-3.54\)
Then, substitute into the formula: \(y = 117.6+( - 3.54)(30 - 27)\)

Step3: Calculate the value

\(y=117.6+( - 3.54)\times3\)
\(y = 117.6-10.62\)
\(y = 106.98\)

Answer:

107.0 (rounded to the nearest hundredth)