Question

What is the average rate of change of the function f(x)=20(14)xf(x)=20(14)x from x = 1 to x = 2? Enter your answer, as a decimal, in the box. Do not round your answer.

Answer 1

dude was right but there ya go

Explanation:

Answer 2

Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:

`A(x) = (f(b)-f(a))/(b-a)`

Given the function:

`f(x) = 20 \cdot((1)/(4))^x`

We have to find the average rate of change from x = 1 to x= 2

At x = 1

then;

`f(x) = 20 \cdot((1)/(4))^1 = 5`

At x = 2

then;

`f(x) = 20 \cdot((1)/(4))^2=20 \cdot (1)/(16) = 1.25`

Substitute these in above formula we have;

`A(x) = (f(2)-f(1))/(2-1)`

⇒
`A(x) = (1.25-5)/(1)=-3.75`

therefore, average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75