For f(x) = 0.01(2)^x, find the average rate of change from x = 2 to x = 10.
A.1.275
B.8
C.10.2
D.10.24
To find the average rate of change, we need to calculate the change in the function value divided by the change in x.
First, let's find the function values at x = 2 and x = 10.
For x = 2:
f(2) = 0.01 * 2^2 = 0.01 * 4 = 0.04.
For x = 10:
f(10) = 0.01 * 2^10 = 0.01 * 1024 = 10.24.
Next, let's find the change in the function value (Δf) and the change in x (Δx).
Δf = f(10) - f(2) = 10.24 - 0.04 = 10.20.
Δx = 10 - 2 = 8.
Finally, we can calculate the average rate of change using the formula:
Average rate of change = Δf / Δx = 10.20 / 8 = 1.275.
Therefore, the average rate of change from x = 2 to x = 10 is A. 1.275.
To find the average rate of change from x = 2 to x = 10 for the function f(x) = 0.01(2)^x, we can use the formula:
Average rate of change = (f(10) - f(2)) / (10 - 2)
First, let's find f(10) and f(2):
f(10) = 0.01(2)^10 = 0.01 * 1024 = 10.24
f(2) = 0.01(2)^2 = 0.01 * 4 = 0.04
Now we can plug these values into the formula:
Average rate of change = (10.24 - 0.04) / (10 - 2)
= 10.20 / 8
= 1.275
Therefore, the average rate of change from x = 2 to x = 10 is approximately 1.275.
So, the correct answer is A. 1.275.
Thank You
when x = 10, y = .01*1024 = 10.24
when x = 2 , y = .01* 4 = .04
change in y = 10.2
change in x = 8
10.2/8 = 1.275