Question

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

Answer 1

0.496

Explanation:

ƒ(x) = 0.01(2)ˣ

1. Calculate the values of f(3) and f(8)

f(3) = 0.01(2)³ = 0.01 × 8 = 0.08

f(8) = 0.01(2)⁸ = 0.01 × 256 = 2.56

2. Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = (2.56 - 0.08)/(8 - 3) =2.48/5 = 0.496

The average rate of change is 0.496.

In the figure below, the red curve represents the function ƒ(x), while the black dashed line represents the average rate of change over the interval [3,8].