Question

Find average rate of change PLEASE HELP
2001-43.0%
2002-44%
2003-45.2%
2004-45.9%
2005-47.1%
2006-48.6%
2007-49.2%
2008-49.3%
2009-48.6%
2010-48%
2011-48.3%
Use data to find avg rate of change in percentage of women in med school from 2001-2008

Answer 1

So the change between 2001-2008 is a total of 6.3

Answer 2

Now find the percentage according to the 8 years.

Answer 3

how do i do that?

Answer 4

spose year the first year 1

year1: 1
year2: 1(1+r1)
year3: 1(1+r1)(1+r2)
year4: 1(1+r1)(1+r2)(1+r3)

year_n: 1(1+r1)(1+r2)(1+r3)...(1+r_{n-1})

is the population after n years

Answer 5

year_a - year_b
------------- is therefore the average rate of change if memory serves
2

Answer 6

memory is kinda foggy these days tho

Answer 7

\[\Large\rm ave~rate~of~change=\frac{(\text{%}~of~2008)-(\text{%}~of~2001)}{2008-2001}\]
Calculate the total % that changed over those years,
then divide that percent by the # of years that occurred in that gap,

And the value you're left with is the average percent each year over those 7 years.
That's how I would approach it at least :)

Remember how to do slope miss britt?

Answer 8

oh its percent on top? i was flipping it. I got 6.3/7 then

Answer 9

Ok good. Remember though, your 6.3 is actually 6.3%

Answer 10

So if you wanna tap tap tap into the calculator, you first need a decimal value.

Answer 11

.063

Answer 12

Ok good, so popping all that info into your calculator should spit out
0.009

Or

as a percent 0.9%

Answer 13

This is telling us that the amount of women in med school was increasing at an average rate of just under 1% each year from the years 2001 to 2008.

Answer 14

And if you look at the numbers, that should make sense.
From 2001 to 2002, it went up 1%
from 2002 to 2003, it went up another 1.2%
2003 to 2004, another 0.7%
and so on.

Answer 15

ah, i see. I didn't realize it was that simple. :) thank you!

Answer 16

got it? yay team \c:/

Answer 17

im getting a different result. last time i used a slope formula on percentages it was wrong. is there something different between this and an average growth rate?

Answer 18

Mmm I don't think there would be a difference D:
Do you have example handy?

Answer 19

i was looking for one i did earlier, but i cant find it in my history

but it went along the lines of doing this:

1(1+.44)(1+.452)(1+.459)(1+.471)(1+.486)(1+.492)(1+.493) = 1(1+r)^7

and solving for r

Answer 20

but this reasoning used population numbers and stabalizes it over the time period

Answer 21

spose we had a population that increased by 30% one year, and 40% the next year

what is the average rate of increase?
1(1.3)(1.4)

the population change was .82 over 2 years which resulted in an average of .41 as what was deemed correct which doesnt get us a (1+r)^2 results, just a 1+r

which was simply why i was wondering about this. im open to being mistaken

Answer 22

http://www.investinganswers.com/financial-dictionary/investing/average-annual-growth-rate-aagr-2549

now this one is saying add up and divide ... as in finding the mean

Answer 23

I think I'm understanding what you're saying >.<
Just trying to think of .. words lol

So the 1+r represents our growth rate?

Answer 24

Err r is our growth rate, the 1 is just the base amount.
ok ok ok :3

Answer 25

r represents the growth rate, like compound interest

Answer 26

Future amount = Present amount, times (1+r)^(n-1) for some n number of years

Answer 27

if we know where we start, and where we end

(n-1) root( F/P ) - 1 = r

Answer 28

So that growth rate is compounding since we're using it over and over.

I don't think that's what was happening in Britt's problem.
The problem was more confusing since they gave us percentages maybe.

But at least the way I was reading the problem was that all the percentages are based off of some base value, they're not being recalculated every period like with an exponential growth function.

That seems to line up with the level of math she is doing at least, basic slope formula and stuff.

Mmm weird problem :[

Answer 29

ill defer to your judgement then :) but just in case theres a solution to compare with, im getting about 47% as the average rate of growth over the years.