Question

Find the average rate of change of the following function on the given interval. y=5^x on [0,2]

Answer 1

`\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}`

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

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

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

[0,2] is 12.5