Question

how to solve the birth rate in a certain country in 1994 was 14.6 births per thousand population. in 2004 the birth rate was 14.32 births per thousand. let x represent years after 1994 and y represent the birth rate. assume the relationship is linear

Answer 1

Answer:

$y(x)=-0.028x+14.6$

Step-by-step explanation:

We are to write a linear equation that relates y in terms of x

The Birth Rate in 1994 =  14.6 births per thousand population.

The Birth Rate in 2004 =  14.32 births per thousand population.

A linear equation is of the form y=mx+b, where:

• x=Number of Years after 1994
• y=the birth rate
• m=Birth rate per year

Step 1: Determine the birth rate per year

In 1994, x=0, y=14.6 thousands

In 2004, x=10, y=14.32 thousands

$m=\dfrac{14.32-14.6}{10-0}\\=\dfrac{-0.28}{10}\\m=-0.028$

Substituting m into our linear equation, we have:

$y(x)=-0.028x+b$

When x=10, y=14.32

$14.32=-0.028(10)+b\\b=14.32+0.28\\b=14.6$

Therefore, a linear equation that relates y in terms of x is:

$y(x)=-0.028x+14.6$