Answer
$-\$6.14$ billion per year
Work Step by Step
We are given the function:
$f(t)=0.5079t^2-8.168t+95.08$
Determine the average rate of change of the model from 2010 to 2014 ($t=0$ corresponds to 2010, while $t=4$ corresponds to 2014):
$\dfrac{f(4)-f(0)}{4-0}=\dfrac{[0.5079(4^2)^2-8.168(4)+95.08]-[0.5079(0^2)^2-8.168(0)+95.08]}{4}$
$=\dfrac{70.5344-95.08}{4}$
$=\dfrac{-24.5456}{4}$
$=-6.1364$
Therefore, the department spending decreased by approximately $\$6.14$ billion each year from 2010 to 2014.
