In the interval
[tex]1\le x\le5[/tex]we can see that
[tex]\begin{gathered} x=1\Rightarrow y=f(x)=9 \\ x=2\Rightarrow y=f(x)=27 \\ x=3\Rightarrow y=f(x)=81 \\ x=4\Rightarrow y=f(x)=243 \\ x=5\Rightarrow y=f(x)=729 \end{gathered}[/tex]in ordet to find the average rate of change, we must compute the slope m:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where, we can choose 2 point of the above set. For instance,
[tex]\begin{gathered} (x_1,y_1)=(1,9) \\ \text{and} \\ (x_2,y_2)=(5,729) \end{gathered}[/tex]Hence,
[tex]\begin{gathered} m=\frac{729-9}{5-1} \\ m=\frac{720}{4} \\ m=180 \end{gathered}[/tex]therefore, the average rate of change is 180
