Answer
$a.\quad -0.1$ percent per year.
In the period 2003-2009, the percentage of the US Discretionary budget allocated to education decreased at an average rate of $ 0.1$ percent per year.
$b.\quad -0.2$ percent per year.
In the period 2005-2009, the percentage of the US Discretionary budget allocated to education decreased at an average rate of $ 0.2$ percent per year.
Work Step by Step
The average rate of change of $f$ over the interval $[a, b]$ is given as:
Average rate of change of $f\displaystyle \ \ =\frac{f(b)-f(a)}{b-a}$
The units of the average rate of change of $f$ are units of $f(x)$ per unit of $x$.
$a.$
Average rate of change of $f\ \ $ over $[3,9]$ is
$\displaystyle \frac{f(9)-f(3)}{9-3}=\frac{6.2-6.8}{6}=\frac{-0.6}{6}=-0.1$ percent per year.
In the period 2003-2009, the percentage of the US Discretionary budget allocated to education decreased at an average rate of $ 0.1$ percent per year.
$b.$
Average rate of change of $f\ \ $ over $[5,9]$ is $\displaystyle \frac{f(9)-f(5)}{9-5}=\frac{6.2-7}{4}=\frac{-0.8}{4}=-0.2$ percent per year.
In the period 2005-2009, the percentage of the US Discretionary budget allocated to education decreased at an average rate of $ 0.2$ percent per year.
