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:

$Average \ Rate \ of \ Change= \frac{f(b)-f(a)}{b-a}$

Given the function

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

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

$\frac{f(2)-f(1)}{2-1} = \frac{20(14)^2-20(14)^1}{1} \\ \\ =20(196-14)=20(182)=3,640$