Question

he power in megawatts that a power plant produces x hours after midnight on a hot summer day is given by the exponential functionwhat is the average rate of change, in megawatts per hour, on the time interval [4,12]

Answer 1

Average rate of change: slope

First, we have to calculate the y values, from the x values given:

x1=4

Replace on the function:

f(x)= 10 (2)^x/4

f(4)= 10 (2)^4/4

f(4)= 10 (2)^1

f(4)= 10 (2)

f(4)= 20

y1= 20

x2=12

f(12)=10 (2)^12/4

f(12)= 10 (2) ^3

f(12)= 10 (8)

f(12)= 80

y2= 80

Apply the slope formula:

`m=(y2-y1)/(x2-x1)`

Replace:

`m=(80-10)/(12-4)=(70)/(8)=8.75`

rate of change : 8.75