Using Estimation to Check Your Answer

Date: 03/28/2008 at 19:45:06
From: Chanice
Subject: percent of increase in population

What was the percent of increase in population from 1950 to 2000.  In
1950 it was 38,000,000 and in 2000 it was 515,000,000.  The increase
was 477,000,000 but when I try to get a percentage I keep getting like
1,255%.

What I find difficult is the fact that my percentage is so high and I 
don't think that my answer is correct and I want to find out what I 
might have done wrong in the problem.  I've worked this particular 
problem about 3 times and still get the same answer and I'm so 
frustrated.

Date: 03/28/2008 at 21:01:37
From: Doctor Peterson
Subject: Re: percent of increase in population

Hi, Chanice.

Your answer sounds reasonable to me!

An increase of 1000% would mean that the increase was 10 times the
original value, so with 1255% the new value would be more than 12 
times the original.  Since 12 times 38 is about 12 times 40, or 480,
and 515 is over that, it's certainly in the right ballpark, so to speak.

Percentages this high are unusual, but that doesn't make them wrong.
You just need to look at the data and see whether an unusual answer is
to be expected.  Since 515 million is many times 38 million, we can
expect the percent increase to be huge.  Knowing how to do such a
"sanity check" is a good way to preserve your sanity when you're doing
a problem like this!

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/29/2008 at 02:08:43
From: Chanice
Subject: Thank you (percent of increase in population)

Thank you Dr. Peterson for helping me with this problem because it was
really beginning to drive me crazy.  I learned new ways to look at 
problems and to do a "sanity check".  So again I just wanted to say
thanks.

Chanice