Question

the following table shows the births per thousand individuals for human females of various ages in 2011.
age in years births per 1000
12 0.6
17 42.5
22 106.4
27 117.6
32 99.9
37 47.5
42 9.5
to the nearest hundredth, how many births per 1000 are there for women who are 35 years old?

Explanation:

Step1: Assume a linear relationship between ages 32 and 37

Let \(x\) be the age and \(y\) be the births per 1000. We have two points \((x_1,y_1)=(32,99.9)\) and \((x_2,y_2)=(37,47.5)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{47.5 - 99.9}{37 - 32}=\frac{-52.4}{5}=-10.48\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

We want to find \(y\) when \(x = 35\). Substitute \(x_1 = 32\), \(y_1 = 99.9\), \(m=-10.48\) and \(x = 35\) into \(y - y_1=m(x - x_1)\). Then \(y-99.9=-10.48\times(35 - 32)\).

Step3: Calculate the value of \(y\)

\(y-99.9=-10.48\times3\). \(y-99.9=-31.44\). \(y=99.9-31.44 = 68.46\)

Answer:

68.46