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: Determine the relationship between age and birth rate

We assume a linear relationship between age \(x\) and birth rate \(y\). Let's take two points \((x_1,y_1)=(32,99.9)\) and \((x_2,y_2)=(37,47.5)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substitute \(x_1 = 32,y_1=99.9,x_2 = 37,y_2 = 47.5\)

$$ m=\frac{47.5-99.9}{37 - 32}=\frac{-52.4}{5}=- 10.48 $$

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((x_1,y_1)=(32,99.9)\) and \(m=-10.48\), the equation is \(y-99.9=-10.48(x - 32)\)

Step4: Substitute \(x = 35\) into the equation

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Answer:

\(68.46\)