For f(x) = 0.01(2)^x, find the average rate of change from x = 3 to x = 8.
0.08, 0.426, 2.48, 5

Solution:

Given f(x) = 0.01(2)^x ; (a, b) =(3, 8)

To find the average rate of change, we divide the change in y(output) by the change in x(input).

Average rate of change = {f(b) - f(a)}/(b - a)

f(b)= f(10) = 0.01(2)⁸ = 0.01(256) = 2.56

f(a) = f(3) = 0.01(2)³ = 0.08

Average rate of change  = {0.01(2)⁸ - 0.01(2)³}/(8 - 3)

= {2.56 - 0.08}/5

= 2.48/5

= 0.496

For f(x) = 0.01(2)^x, find the average rate of change from x = 3 to x = 8.

Summary:

The average rate of change from x = 2 to x = 8 for function f(x) = 0.01(2)^x is 0.0.496