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How to calculate the rate of decay

Updated September 03, 2018

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.

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

  2. Use the calculator to take the natural log (often abbreviated "ln" on calculators) of the result from Step 1. In this example, you would take the natural log of 0.8, which equals -0.223143551.

  3. Divide the result from Step 2 by 2 to calculate the rate of decay. In this example, you would divide -0.223143551 by 2 to get a rate of decay of -0.111571776.

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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."

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