# Taking the average of two average rates of change?

• May 25th 2011, 07:18 PM
CalculusABStudent
Taking the average of two average rates of change?
I am working on a math Jeopardy project for my Calc AB class and I wanted to write a question similar to the following one, but I need to know how to solve it first. Could anyone show me the work to get the answer of 13% per year?
Here is the Question out of my Calc book: The table shows the estimated percentage P of the population of Europe that use cell phones. (Midyear estimates are given).
Year: 1998 1999 2000 2001 2002 2003
P: 28 39 55 68 77 83

Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. What are its units?

So my attempt at this problem was taking the rate of change of 1999 and then 2001 and then taking the rate of change between those two to get the average rate of change of those average rates of change at 2000? ah help please. I was totally off.
• May 25th 2011, 08:32 PM
integral
Just say $\frac{F(b)-F(a)}{b-a}$
Which gives you average slope.
f(x)= percent
f'(x)= rate of percent change
f''(x)=rate of the rate of percent change.
You were looking for an approx of f''(x) I think.
You need f'(x)

b=2001
a=2000
• May 25th 2011, 08:44 PM
CalculusABStudent
I'm still not getting the right answer. I've done 55-39 to get 16. Then I did 68-55 to get 13. Then added 16 and 13 and divided by two and got 14.5. However the answer is 13. I tried a few other methods and got the wrong answer also.

EDIT: nevermind I got it. thank you
• May 25th 2011, 08:56 PM
integral
(68-55)/(2001-2000)

Sorry, I gave you the wrong b and a. That is the answer though. No more work needs to be done.
• May 26th 2011, 03:05 AM
Ackbeet
Is this project for a grade?
• May 26th 2011, 06:11 AM
mr fantastic
Quote:

Originally Posted by CalculusABStudent
I am working on a math Jeopardy project for my Calc AB class and I wanted to write a question similar to the following one, but I need to know how to solve it first. Could anyone show me the work to get the answer of 13% per year?
Here is the Question out of my Calc book: The table shows the estimated percentage P of the population of Europe that use cell phones. (Midyear estimates are given).
Year: 1998 1999 2000 2001 2002 2003
P: 28 39 55 68 77 83

Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. What are its units?

So my attempt at this problem was taking the rate of change of 1999 and then 2001 and then taking the rate of change between those two to get the average rate of change of those average rates of change at 2000? ah help please. I was totally off.