Find the average rate of change from x = 10 to x =17 for the function f(x) = 0.01(2) ^x and select the correct answer below

A. 10.24
B. 185.78
C. 1300.48
D. 1310.72

Is it A?

f ( 17 ) = 0.01 ( 2 ) ^ x =

0.01 ( 2 ) ^ 17 =

0.01 * 131072 =

1310.72

f ( 10 ) = 0.01 ( 2 ) ^ x =

0.01 ( 2 ) ^ 10 =

0.01 * 1024 =

10.24

The average rate of change :

[ f ( 17 ) - f ( 10 ) ] / ( 17 - 10 ) =

[ f ( 17 ) - f ( 10 ) ] / 7 =

( 1310.72 - 10.24 ) / 7 =

1300.48 / 7 =

185.78286

Approx. = 185.78

Answer B

Nope.

You want

f(17)-f(10)
---------------
17-10

that would be 7. What do I do now?

Thank you so much by the way

@steve

Wait, so its 1300.48?

No, it's B!

Why not show your work, so we can see what's going on?

How did you evaluate .01 * 2^17?

What i did to get c is f(10) = 0.01 (2) ^10 which was 10.24 then f(17) = 0.01 (2) ^17 which equals 1310.72 then subtracted and got 1300.48

But now I see it says average change, so you would then divide 1300.48 by 7 which gets 185.78. Right? @steve

okay thank you

To find the average rate of change of a function from x = 10 to x = 17, you need to calculate the difference in the function values at these two points and divide it by the difference in x-values.

First, let's find f(10):

f(10) = 0.01(2)^10
= 0.01(1024)
= 10.24

Next, let's find f(17):

f(17) = 0.01(2)^17
= 0.01(131,072)
= 1,310.72

Now, let's calculate the average rate of change:

Average rate of change = (f(17) - f(10)) / (17 - 10)
= (1310.72 - 10.24) / 7
= 1300.48 / 7
= 185.78

Therefore, the correct answer is B. 185.78.