How to Calculate the Rate of Decay

By Mark Kennan
Bacteria Colonies image by ggw from

Decay measures how quickly something disappears or dies. Decay is often used to quantify the exponential decrease of bacteria or nuclear waste. In order to calculate exponential decay, you need to know the initial population and final population. Exponential decay occurs when the amount of decrease is directly proportional to how much exists.

Step 1

Divide the final count by the initial count. For example, if you had 100 bacteria to start and 2 hours later had 80 bacteria, you would divide 80 by 100 to get 0.8.

Step 2

Use the calculator to take the natural log (often abbreviated "ln" on calculators) of the result from the previous step. In this example, you would take the natural log of 0.8, which equals -0.223143551.

Step 3

Divide the result from the last step by the number of time periods to find the rate of decay. In this example, you would divide -0.223143551 by 2, the number of hours, to get a rate of decay of -0.111571776. As the time unit in the example is hours, the decay rate is -0.111571776 per hour.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."