Q15. - Algebra 1

Question

In 1980, the population of Kentucky was about $\mathbf{3}\mathbf{.66}$ million people. By 2000, this number had grown to about $\mathbf{4.04}$ million people. What was the annual rate of change in population from 1980 to 2000?

Step-by-Step Solution

Answer

The annual rate of change in population from 1980 to 2000 was $\mathbf{0}\mathbf{.019}$ million/year.

Step 1. Write the formula for the annual rate of change of population.

The formula for the annual rate of change of population is:

$\text{annual rate of change of population}=\frac{\text{change in population}}{\text{change in time}}$

Step 2. Find the annual rate of change in population from 1980 to 2000 .

It is given that in 1980, the population was $3.66$ million and in 2000, the population was $4.04$ million.

Therefore, it can be noticed that:

$\begin{array}{c}\text{change in population}=(4.04-3.66)\text{ million}\\ =0.38\text{ million}\end{array}$

$\begin{array}{r}\text{change in time}=(2000-1980)\text{ year}\\ =20\text{ year}\end{array}$

Now substitute these values in the formula for the annual rate of change of population.

Therefore, it is obtained that:

$\begin{array}{r}\text{annual rate of change of population}=\frac{\text{change in population}}{\text{change in time}}\\ =\frac{0.38\text{ million}}{20\text{ year}}\\ =0.019\text{ million/year}\end{array}$

Therefore, the annual rate of change in population from 1980 to 2000 was $0.019$ million/year.