Answer
$2002-2005$
Work Step by Step
The average rate of change of $f$ over the interval $[a, b]$ is given by:
Average rate of change of $f\displaystyle \ \ =\frac{f(b)-f(a)}{b-a}$
Thus, we have:
$\left[\begin{array}{lllll}
a & b & f(b)-f(a) & avg.\ rate & \\
0 & 3 & 1009-956 & 53/3 & (*)\\
1 & 4 & 1008-958 & 50/3 & \\
2 & 5 & 1036-975 & 61/3 & \\
3 & 6 & 1018-1009 & 9/3 & \\
4 & 7 & 1003-1008 & -5/3 & \\
5 & 8 & 1013-1036 & -23/3 & \\
6 & 9 & 1032-1018 & 14/3 & \\
7 & 10 & 1036-1003 & 33/3 &
\end{array}\right]$
Thus, the period with the greatest average rate of change is
$2002-2005$
