Beginning Algebra With Applications, Chapter 5, 5.1, Section 5.1, Problem 36

The following table shows the projected population of adults 18 to 19 years old for selected years from 2005 to 2030.

$\begin{array}{c|cccccc}
\text{Year} & 2005 & 2010 & 2015 & 2020 & 2025 & 2030 \\
\hline\\
\text{Population projection, in millions} & 8.4 & 8.6 & 8.1 & 8.6 & 9.0 & 9.4
\end{array} $

a. Determine the average annual rate of change of the U.S. population of adults 18-18 years old from 2005 to 2030.


$
\begin{equation}
\begin{aligned}

\text{average annual rate of change} =& \frac{\text{population in 2030 - population in 2005}}{2030-2005}
\\
\\
=& \frac{9.4-8.4}{2030-2005}
\\
\\
=& \frac{1}{25}
\\
\\
=& 0.04

\end{aligned}
\end{equation}
$


This means that the population of 18-19 years old from 2005 to 2030 was increased by 40,000 per year.

b. In which five-year period shown did the average annual rate of change of this population decline? What was the average annual rate of change for that period?

The population decline from 2010 to 2015, the average annual rate of change is


$
\begin{equation}
\begin{aligned}

\frac{\text{population in 2015 - population in 2010}}{2015-2010} =& \frac{8.1-8.6}{2015-2010}
\\
\\
=& \frac{-0.5}{5}
\\
\\
=& -0.1

\end{aligned}
\end{equation}
$



The population of 18-19 years old from 2010-2015 was decreased by 100,000 per year.