Answer
(a)
Consider the provided function,
\[f\left( x \right)=782x+6564\] …... (1)
To calculate the average cost of a family health insurance plan in\[2011\], x is:
\[\begin{align}
& x=2011-2000 \\
& =11
\end{align}\]
Put the value of x in equation (1). Then,
\[\begin{align}
& f\left( 11 \right)=\left( 782\times 11 \right)+6564 \\
& =15,166
\end{align}\]
Therefore, the average cost of a family health insurance plan in \[2011\]is\[\$15,166\].
(b)
Consider the provided function,
\[g\left( x \right)=6875{{e}^{0.077s}}\] …... (1)
To calculate the average cost of a family health insurance plan in\[2011\], x is:
\[\begin{align}
& x=2011-2000 \\
& =11
\end{align}\]
Put the value of x in equation (1). Then,
\[\begin{align}
& g\left( 11 \right)=6875{{e}^{\left( 0.077\times 11 \right)}} \\
& =\text{16,036}\text{.889} \\
& \approx \text{16,037}
\end{align}\]
Therefore, the average cost of a family health insurance plan in \[2011\] by exponential model is\[\$16,037\].
(c)
Consider the graph,
The average cost of a family health insurance plan in 2011 is \[\$15,073\].
From the linear model, the average cost of a family health insurance plan in 2011 is \[\$15,166\].
And from the exponential model, the average cost of a family health insurance plan in 2011is \[\$16,037\].
The results obtained by the linear model is much closer to the data represented in the graph than the exponential data.
Therefore, the linear model is better for the data in the year 2011.
