Hence, by using the formula college students spend in $2011$ is $\$ 89.6$. which is overestimates by $ \$ 2.6 $ billion.
Work Step by Step
From the question we have $D(x)=1.2x^2+1.6(x+40)$, Where, $D$ is discretionary spending in billions of dollars and $x$ is years after $2007$. Therefore, the value of $x$ for the year $ 2011 $ is $ =2011-2007 =4 $. plug in $x=4$ into the formula. $D(4)=1.2(4)^2+1.6(4+40)$. Clear the parentheses. $ D(4)=1.2\times 16+6.4+64 $. Simplify. $ D(4)=89.6 $. By observing the graph the value of $D(4)$ is $87$ billions of dollars. Hence, the model overestimates the actual value by $87-89.6=-2.6$ billions of dollars.