What expression is used to determine the overall growth rate of a population?

In 1980, the population in Lane County was 250,000. This grew to 280,000 in 1990. What is the annual percentage growth rate for Lane County?

VPresent = 280,000
VPast = 250,000
N = 10 Years

The population of Lane County grew 12 percent between 1980 and 1990 or at an rate of 1.2 percent annually.

Another common method of calculating rates of change is the Average Annual or Compound Growth Rate [AAGR]. AAGR works the same way that a typical savings account works. Interest is compounded for some period [usually daily or monthly] at a given rate. Here's how it works:

Let's say you had $100 dollars and invested it in an account that paid 5 percent annually. The table below shows how your interest accumulates.

Year

0

1

2

3

4

5

$100

+5%

+5%

+5%

+5%

+5%

NA

$5

$5

$6

$6

$6

$100

$105

$110

$116

$122

$128

This can also be written algebraically as:

[[[[[100 * [1.05] * 1.05] * 1.05] * 1.05] * 1.05]

A. The formula to calculate future population given current population and a growth rate is:

Where:

PopPresent = Present Population
i = Growth Rate
n = Number of Periods

To calculate your future balance in the above example the formula would be:

Future Value = $100 * [1.05]5 = $128

To perform this on a hand-held calculator take the following steps:

Press 1 + i [growth rate in decimal], the = [equals]

Press yx, then n [the number of periods]