For f(x) = 0.01(2)ˣ, find the average rate of change from x = 2 to x = 10.
1.275, 8, 10.2, 10.24

Solution:

Given f(x) = 0.01(2)ˣ

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) ; (a,b) =(2,10)

f(b)= f(10) = 0.01(2)¹⁰ = 10.24

f(a) = f(2) = 0.01(2)² = 0.04

Rate of change = {0.01(2)¹⁰ - 0.01(2)²} / (10-2)

= (10.24 – 0.04) /8

= 10.20/8

= 1.275

For f(x) = 0.01(2)ˣ, find the average rate of change from x = 2 to x = 10.
1.275, 8, 10.2, 10.24

Summary:

The average rate of change from x = 2 to x = 10 for function f(x) = 0.01(2)ˣ is 1.275.