Chapter 7, Problem 2PS

(a)

To determine

To calculate: The percent of the total population of the different age group in $2011$ and $2014$, if the total population $2011$ was $311,721,632$ and the total population in $2014$ was $318,857,056$. The matrices $\begin{array}{c}\text{2011 }\\ \text{0-19 20-64 65+}\\ \begin{array}{c}\text{Male}\\ \text{Female}\end{array}\left[\begin{array}{ccc}42,376,825& 92,983,543& 17,934,267\\ 40,463,751& 94,530,885& 23,432,361\end{array}\right]\end{array}$ and $\begin{array}{c}\text{2014}\\ \text{0-19 20-64 65+}\\ \begin{array}{c}\text{Male}\\ \text{Female}\end{array}\left[\begin{array}{ccc}41,969,399& 94,615,796& 20,351,292\\ 40,166,203& 95,862,447& 25,891,919\end{array}\right]\end{array}$ represent the male and female population in the United States in $2011$ and $2014$ in three different age groups, respectively.

(b)

To determine

To calculate: The change in percent of the population from $2011$ to $2014$ for each gender and age group in the form of a matrix, if the total population in $2011$ was $311,721,632$ and the total population in $2014$ was $318,857,056$. The matrices $\begin{array}{c}\text{2011 }\\ \text{0-19 20-64 65+}\\ \begin{array}{c}\text{Male}\\ \text{Female}\end{array}\left[\begin{array}{ccc}42,376,825& 92,983,543& 17,934,267\\ 40,463,751& 94,530,885& 23,432,361\end{array}\right]\end{array}$ and $\begin{array}{c}\text{2014}\\ \text{0-19 20-64 65+}\\ \begin{array}{c}\text{Male}\\ \text{Female}\end{array}\left[\begin{array}{ccc}41,969,399& 94,615,796& 20,351,292\\ 40,166,203& 95,862,447& 25,891,919\end{array}\right]\end{array}$ represent the male and female population in the United States in $2011$ and $2014$ in three different age groups, respectively.

(c)

To determine

Which gender $\left(s\right)$ and age group $\left(s\right)$ observed percentage decrease from $2011$ to $2014$ with reference to the result from part $\left(b\right)$.