Answer
See below:
Work Step by Step
(a)
Consider the information provided,
If \[x\] denotes the number of years, then the function for U.S. adults living alone,\[y\], can be expressed as sum of U.S. adults living alone and the product of rate of increasing and number of years.
The function can be shown as follows for U.S. adults living alone:
\[y=5+0.2x\]
Thus, the obtained function is\[y=5+0.2x\].
The function for U.S. adults living alone,\[y\], after \[x\]years can be expressed as \[y=5+0.2x\].
(b)
Consider the information provided,
If \[x\] denotes the number of years, then the function for married U.S. adults living with kids,\[y\], can be expressed as sum of married U.S. adults and product of rate of decreasing and number of years.
The function can be shown as follows for married U.S. adults:
\[y=47-0.4x\]
Thus, the obtained function is\[y=47-0.4x\].
The function for married U.S. adults living with kids,\[y\], after \[x\] can be expressed as \[y=47-0.4x\]
(c)
Consider the information provided,
The year in which adults belonging to both the groups will be equal can be found by equating the functions for both the groups
\[\begin{align}
& 5+0.2x=47-0.4x \\
& 0.6x=42 \\
& x=70
\end{align}\]
The percentage of each group can be calculated by substituting this value in the function for that group.
The percentage of married U.S. adults living with kids
\[\begin{align}
& y=47-0.4x \\
& =47-0.4\times 70 \\
& =19
\end{align}\]
The percentage of U.S. adults living alone
\[\begin{align}
& y=5+0.2x \\
& =5+14 \\
& =19
\end{align}\]
Thus, the percentage of U.S adults belonging to each group is \[19%\].
