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.

Answer 1

The average rate of a function f(x) over an interval x = a and x = b is given by:


`Average \ Rate \ of \ Change= (f(b)-f(a))/(b-a)`

Given the function


`f(x)=20(14)^x`

The average rate of change from x = 1 to x = 2 is given by:


`(f(2)-f(1))/(2-1) = (20(14)^2-20(14)^1)/(1) \\ \\ =20(196-14)=20(182)=3,640`