Answer
Hence, the college students spend in 2013 is $ \$ 116.8 $ billion. The model underestimates by $ \$0.2 $ billion.
Work Step by Step
The given formula is
$D(x)=1.2x^2+1.6(x+40)$, Where, $D$ is discretionary spending in billions of dollars and $x$ is years after $2007$.
Therefore, the value of $x$ for the year $ 2013 $ is $ =2013-2017 =6 $.
plug in $x=6$ into the formula.
$D(6)=1.2(6)^2+1.6(6+40)$.
Clear the parentheses.
$ D(6)=1.2\times 36+9.6+64 $.
Simplify.
$ D(6)=116.8 $.
By observing the graph the value of $D(6)$ is $117$ billions of dollars.
Hence, the model underestimates the actual value by $117-116.8=0.2$ billions of dollars.
