Answer
$2004-2006$
Work Step by Step
Average rate of change of $f\ \ $ over $[0,2]$ is
$\displaystyle \frac{f(2)-f(0)}{2-0}=\frac{4-3}{2}=\frac{1}{2}=0.5$ percentage points per year
Average rate of change of $f\ \ $ over $[2,4]$ is
$\displaystyle \frac{f(4)-f(2)}{4-2}=\frac{8-4}{2}=\frac{4}{2}=2.0$ percentage points per year
Average rate of change of $f\ \ $ over $[4,6]$ is
$\displaystyle \frac{f(6)-f(4)}{6-4}=\frac{13-8}{2}=\frac{5}{2}=2.5$ percentage points per year
Average rate of change of $f\ \ $ over $[6,8]$ is
$\displaystyle \frac{f(8)-f(6)}{8-6}=\frac{13.8-13}{2}=\frac{0.8}{2}=0.4$ percentage points per year
The average rate of change was the greatest over $[4,6]$, which corresponds to the $2004-2006$ two-year period.
