- "A(t)=" is the same as "y=".
- "a" in this formula represents the initial population of the area you are calculating for.
- "1" is a constant, and always has a value of one.
- "r" is the growth rate of the area you are calculating for in the form of a decimal. For example, a 3% growth rate would become .03.
- "^t" is an exponent representing the amount of time you are projecting for, measured in years. For example, if you are using 2010 Census information and calculating for 2020, the exponent would be 10.
- An example equation: Finding the current United States population from the first Census, conducted in 1790.
- The population at the first Census was 3,929,214 people. Since then, the American population has grown by approximately 2.03% annually.
- Therefore, the equation would be as follows: A(t)=3,919,214(1+.0203)^226
- Plugging this into a calculator, you end up with 367,875,920 as the population for 2016. The actual estimate is 322,369,319, which shows that the growth rate we used is out of date, or inaccurate.
- This discrepancy shows the usefulness of this formula in detecting errors in calculation for applications.