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.