[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)=2(3)^x \qquad
\begin{cases}
x_1=0\\
x_2=1
\end{cases}\implies \cfrac{f(1)-f(0)}{1-0}\implies \cfrac{2(3)^1-2(3)^0}{1}\\\\
-------------------------------\\\\
f(x)=2(3)^x \qquad
\begin{cases}
x_1=2\\
x_2=3
\end{cases}\implies \cfrac{f(3)-f(2)}{3-2}\implies \cfrac{2(3)^3-2(3)^2}{1}[/tex]
part B)
how many times? 9 times larger
how so? well, is an exponential function, anything raised at the 0 exponent, is 1, no matter what the number is
and anything raised at the 1 exponent is itself, no matter what number it is
after 0 and 1, the base number is multiplying itself that many times, and that's a larger value.
