The table shows the numbers $a _ { n }$ (in thousands)of residents from 2002 through 2007. $$\begin{array} { | c | l | }
\hline & \text { Number of residents, } \
&.\
{ \text { Year } }& a _ { n } \
&.\
\hline 2002 & 646 \
\hline 2003 & 657 \
\hline 2004 & 668 \
\hline 2005 & 679 \
\hline
\end{array}$$ $$\begin{array} { | l | l | }
\hline 2006 & 690 \
\hline 2007 & 701 \
\hline
\end{array}$$
Determine whether a linear model can be used to approximate the data.
If so,find a model algebraically.Let n represent the year,with $n = 2$ corresponding to 2002.
A)A linear model can be used. $a _ { n } = 11 n + 690$
B)A linear model can be used. $a _ { n } = 11 n + 657$
C)A linear model can be used. $a _ { n } = 11 n + 701$
D)A linear model can be used. $a _ { n } = 11 n + 624$
E)A linear model can be used. $a _ { n } = 11 n + 646$

Question

The table shows the numbers $a _ { n }$ (in thousands)of residents from 2002 through 2007. $$\begin{array} { | c | l | } 
\hline  & \text { Number of residents, } \
&.\
{ \text { Year } }& a _ { n } \
&.\
\hline 2002 & 646 \
\hline 2003 & 657 \
\hline 2004 & 668 \
\hline 2005 & 679 \
\hline
\end{array}$$ $$\begin{array} { | l | l | } 
\hline 2006 & 690 \
\hline 2007 & 701 \
\hline
\end{array}$$
Determine whether a linear model can be used to approximate the data.
If so,find a model algebraically.Let n represent the year,with $n = 2$ corresponding to 2002.
A)A linear model can be used. $a _ { n } = 11 n + 690$
B)A linear model can be used. $a _ { n } = 11 n + 657$
C)A linear model can be used. $a _ { n } = 11 n + 701$
D)A linear model can be used. $a _ { n } = 11 n + 624$
E)A linear model can be used. $a _ { n } = 11 n + 646$

Quizplus · Accepted Answer

The data shows a consistent increase of 11,000 residents each year. To find the model, we can use the year 2002 as a reference point where $n = 2$. For 2002, $a_n = 646$, so substituting $n = 2$ into the equation $a_n = 11n + b$ gives us $646 = 22 + b$, solving for $b$ gives $b = 624$. Therefore, the model is $a_n = 11n + 624$.

The Table Shows the Numbers ana _ { n }an​ (In Thousands)of Residents from 2002 Through 2007

The Table Shows the Numbers $a _ { n }$ (In Thousands)of Residents from 2002 Through 2007