Answer
$12$
Work Step by Step
The average rate of change from $x=a$ to $x=b$ is given by the formula:
$$\dfrac{f(b)-f(a)}{b-a}$$
The average rate of change of $f(x)=9^x$ from $a=\frac{1}{2}=0.5$ to $b=1$ is:
\begin{align*}&=\dfrac{f(1)-f\left(\frac{1}{2}\right)}{1-\frac{1}{2}}\\
\\&=\dfrac{9^{1}-9^{\frac{1}{2}}}{1 / 2}\\
\\&=\dfrac{9-\sqrt{9}}{\frac{1}{2}}\\
\\&=\dfrac{9-3}{\frac{1}{2}}\\
\\&=\dfrac{6}{\frac{1}{2}}\\
\\&=6 \cdot \frac{2}{1}\\
\\&=12
\end{align*}
