Answer
$2006-2008$
Work Step by Step
Average rate of change of $f\ \ $ over $[0,2]$ is
$\displaystyle \frac{f(2)-f(0)}{2-0}=\frac{500-400}{2}=\frac{100}{2}=50$ billion per year.
Average rate of change of $f\ \ $ over $[2,4]$ is
$\displaystyle \frac{f(4)-f(2)}{4-2}=\frac{900-500}{2}=\frac{400}{2}=200$ billion per year.
Average rate of change of $f\ \ $ over $[4,6]$ is
$\displaystyle \frac{f(6)-f(4)}{6-4}=\frac{1200-900}{2}=\frac{300}{2}=150$ billion per year.
Average rate of change of $f\ \ $ over $[6,8]$ is
$\displaystyle \frac{f(8)-f(6)}{8-6}=\frac{1250-1200}{2}=\frac{50}{2}=25$ billion per year.
The average rate of change was the least over $[6,8]$, which corresponds to the $2006-2008$ two-year period.
