Respuesta :

[tex]\begin{gathered} \text{ Given y=5}^x \\ \text{ We want to find the average rate of change on the interval \lbrack{}0,2\rbrack} \\ \text{When x = 2, we have } \\ y=5^2=25 \\ \text{When x=0} \\ y=5^0=1 \\ \end{gathered}[/tex]

To find the rate of change within this interval, we have

[tex]\begin{gathered} \text{ Rate of change =}\frac{f(2)-f(0)}{2-0} \\ =\frac{25-0}{2-0} \\ =\frac{25}{2} \\ =12.5 \end{gathered}[/tex]

Hence, the average rate of change of the function within the interval

[0,2] is 12.5

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