Question

The power in megawatts that power plant produces x hours after midnight on a hot summer day is given by the exponential function
`f(x) = 10(2) (x)/(4)`what is the average rate of change in megawatts per hour on the time interval [4,12]?

Answer 1

`f(x)=10(2)^{(x)/(4)}`

To find the average rate of change you need to find the value of the function in those values of x:

`(\Delta f(x))/(\Delta x)=(f(x_2)-f(x_1))/(x_2-x_1)`

If x is 4: You can find the value of f(4) with the graph. The value that have the function (y) in x=4

`f(4)=20`

If x is 12:

`f(12)=80`

Then, the average rate of change is:

`\begin{gathered} (\Delta f(x))/(\Delta x)=(f(12)-f(4))/(12-4) \\ \\ =(80-20)/(12-4) \\ \\ =(60)/(8)=(30)/(4)=(15)/(2) \end{gathered}`The average rate of change is 15/2 or 7.5 megawatts per hour