Answer
See the explanation below.
Work Step by Step
(a)
We know that the objective here is to determine the percentage of seniors who used marijuana in $2010$. As we can see that from the graph, the line that shows the percentage of people using marijuana, for the year 2010, corresponds to $44\%$.
(b)
In year 2010, the value of n will be,
$\begin{align}
& n=2010-1990 \\
& =20
\end{align}$
Now, let us consider the following formula:
$M=0.1n+43$
So, after substituting $n=20$ in the above formula, we get:
$\begin{align}
& M=0.1n+43 \\
& =0.1\left( 20 \right)+43 \\
& =2+43 \\
& =45
\end{align}$
Therefore, the percentage of seniors who used marijuana in $2010$, calculated by using the formula is $45\%$. This value is almost equal to the value obtained through the graph, which is $44\%$.
(c)
We know that the objective here is to determine the percentage of seniors who used alcohol in $2010$. As we see from the above graph, the line that shows the percentage of people using alcohol, for the year 2010, corresponds to $71\%$.
(d)
Now, in year 2010, value of n will be as follows:
$\begin{align}
& n=2010-1990 \\
& =20
\end{align}$
Let us consider the following formula:
$A=-0.9n+88$
So, after substituting $n=20$ in the above formula, we get:
$\begin{align}
& A=-0.9n+88 \\
& =-0.9\left( 20 \right)+88 \\
& =-18+88 \\
& =70
\end{align}$
Therefore, the percentage of seniors who used alcohol in $2010$, calculated by using the formula is $70\%$. This value is almost equal to the value obtained through the graph, which is $71\%$.
(e)
We know that the objective here is to determine the year where marijuana consumption is maximum. As we can see from the given graph, the point where the percentage is maximum, can be seen as for the year 2000. The value of the percentage is $49\%$.
The percentage of seniors having maximum consumption of marijuana is in the year $2000$ and is approximately equal to $49\%$.
