Points on the curve given below can be denoted as,
[tex]\begin{gathered} (x_2,y_2)=(2,45) \\ (x_1,y_1)=(1,15) \end{gathered}[/tex][tex]\begin{gathered} \text{Where,} \\ \text{slope m =}\frac{y_2-y_{1_{}}}{x_2-x_1} \end{gathered}[/tex]Substituting the variables into the equation,
[tex]\begin{gathered} m=\frac{45-15}{2-1}=\frac{30}{1}=30 \\ m=30 \end{gathered}[/tex]To find the average rate change of the function over (0,2),
[tex]\text{Average rate change =}\frac{\text{Slope}}{b-a}[/tex][tex]\begin{gathered} (a,b)=(0,2) \\ \text{Average rate change=}\frac{30}{2-0}=\frac{30}{2}=15 \end{gathered}[/tex]Hence, the average rate change of the function over the interval (0,2) is A "15".
