[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}\\\\
-------------------------------[/tex]
[tex]\bf \stackrel{section~A}{gf(x)=4(3)^x \qquad
\begin{cases}
x_1=1\\
x_2=2
\end{cases}}\implies \cfrac{g(2)-g(1)}{2-1}\implies \cfrac{4(3)^2-4(3)^1}{1}
\\\\\\
\cfrac{36-12}{1}\implies \boxed{24}
\\\\\\
\stackrel{section~B}{gf(x)=4(3)^x \qquad
\begin{cases}
x_1=3\\
x_2=4
\end{cases}}\implies \cfrac{g(4)-g(3)}{4-3}\implies \cfrac{4(3)^4-4(3)^3}{1}
\\\\\\
\cfrac{324-108}{1}\implies \boxed{216}[/tex]
part B) well, you already know.
why is that? well, because 4(3)ˣ is an exponential function, so the jumps from one point to another are large.
