To find the average rate of change of the function f(x) = 0.01 * 2^x over the interval from x = 2 to x = 10, we first need to calculate the function’s values at those two points.
1. Calculate f(2):
f(2) = 0.01 * 2^2 = 0.01 * 4 = 0.04
2. Calculate f(10):
f(10) = 0.01 * 2^10 = 0.01 * 1024 = 10.24
Now we can find the average rate of change using the formula:
Average Rate of Change = (f(b) – f(a)) / (b – a)
Here, a = 2 and b = 10:
Average Rate of Change = (f(10) – f(2)) / (10 – 2)
= (10.24 – 0.04) / (10 – 2)
= 10.20 / 8
= 1.275
Therefore, the average rate of change of the function from x = 2 to x = 10 is 1.275.