Question

What is the average rate of change of the function on the interval from x = 0 to x = 5 f(x)=

1/2(3)x

Answer 1

What is the average rate of change of the function on the interval from x = 0 to x = 5 ; f(x)= 1\2 (3)^x

Answer:

Average rate of change of the function on the interval from x = 0 to x = 5 is 24.2

Solution:

Given function is:

`f(x) = (1)/(2)(3^x)`

We have to find the average rate of change of function from x = 0 to x = 5

The formula for average rate of change can be expressed as follows:

`{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}`

So for rate of change of function from x = 0 to x = 5 is:

`{A\left( x \right) = \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}}`

Let us find f(0) and f(5)

To find f(0), substitute x = 0 in f(x)

`f(0) = (1)/(2)(3^0) = (1)/(2)`

To find f(5), substitute x = 5 in f(x)

`f(5) = (1)/(2)(3^5) = (1)/(2)(243) = (243)/(2)`

Therefore,

`A(x)=((243)/(2)-(1)/(2))/(5-0)=(242)/((2)/(5))=(242)/(2) * (1)/(5)=24.2`

Therefore average rate of change of the function on the interval from x = 0 to x = 5 is 24.2