For f(x) = 0.01(2)x, find the average rate of change from x = 2 to x = 10.
the average rate of change is just
(f(10)-f(2))/(10-2)
so, plug and chug.
To find the average rate of change of a function, we need to calculate the difference in the function values and divide it by the difference in the input values.
In this case, we want to find the average rate of change of the function f(x) = 0.01(2)^x from x = 2 to x = 10.
Step 1: Calculate the function values at x = 2 and x = 10:
f(2) = 0.01(2)^2 = 0.01(4) = 0.04
f(10) = 0.01(2)^10 = 0.01(1024) = 10.24
Step 2: Calculate the difference in the function values:
Difference in function values = f(10) - f(2) = 10.24 - 0.04 = 10.20
Step 3: Calculate the difference in the input values:
Difference in input values = 10 - 2 = 8
Step 4: Calculate the average rate of change:
Average rate of change = Difference in function values / Difference in input values
= 10.20 / 8
= 1.275
Therefore, the average rate of change of the function f(x) = 0.01(2)^x from x = 2 to x = 10 is 1.275.