ANSWER:
b) Δf/Δx = 22.5
STEP-BY-STEP EXPLANATION:
To determine the average rate of change, we use the following formula:
[tex]\begin{gathered} r=\frac{\Delta f}{\Delta x} \\ \\ \frac{\Delta f}{\Delta x}=\frac{f(b)-(f(a)}{b-a} \end{gathered}[/tex]
We substitute in each case and get the following:
[tex]\begin{gathered} \frac{\Delta f}{\Delta x}=\frac{3\cdot\left(2\right)^{2\cdot2}-3\cdot\left(2\right)^{2\cdot\:0}}{2-0} \\ \\ \frac{\Delta f}{\Delta x}=\frac{3\cdot2^4-3\cdot2^0}{2} \\ \\ \frac{\Delta f}{\Delta x}=\frac{3\cdot16-3}{2}=\frac{48-3}{2}=\frac{45}{2} \\ \\ \frac{\Delta f}{\Delta x}=22.5 \end{gathered}[/tex]
Therefore, the correct answer is b) Δf/Δx = 22.5
