[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\
f(x)=500(1.05)^x \qquad
\begin{cases}
x_1=2\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(2)}{4-2}
\\\\\\
\cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625[/tex]
