What's in a Number?

I'm starting to review the Town of Cary's 2014 Proposed Budget.  As I was reading through the History of Cary
page, I came across the following:

The 1990 Decennial Census reported the Town's population to be 44,276. The 2000 Decennial Census reported a population of 94,536, indicating a growth rate of 116% since 1990, which was an average of 11.6% per year. The 2010 Decennial Census reported the Town’s population to be 135,234, indicating a growth rate of 43% since 2000, which was an average of 4.3% per year.

Growth Rate Calculation Issues

So what is wrong with "...a growth rate of 116% since 1990, which was an average of 11.6% per year."?  Well you cannot just average the total growth over a decade to find the average growth rate per year.  This is a compounding problem, and you need to know the compounding rate to get an idea as to the average growth rate, or the growth you might read each year in reports of the year past.

From the Cary Census numbers:

• The 1990-2000 growth rate is really 7.88%
• The 2000-2010 growth rate is really 3.64%

Now these growth rates are still pretty big, but they give you more of a sense of how to compare them with the growth projections in the next few years.

The Rule of 72

You may remember this from school.  If you divide 72 by a growth rate (or interest rate on a bank account) you will get the period of time that your amount will double.  This is not exact, but it is good enough for mental math.  The rule used 72, 70 or 69 depending on where you learned it, but it is basically the same rule.

So a 1% growth rate will double the population in 72 years (about a lifetime).  A 10% growth rate will double in 7 years (think starting middle school and graduating high school).

There are lots of calculators that can perform compound growth calculations and that is what I used to calculate the above numbers.

The Takeaway:

You know the old saying "figures lie and liars figure".  I don't think that there was any intention to mislead the reader in this case, but you really need to use the correct numbers and use the proper calculations when you are performing analysis or you can come up with some unwanted results.  Be on your guard!