How to Calculate the Rate of Decay

How to Calculate the Rate of Decay
••• Ca-ssis/iStock/GettyImages

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.

    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.

    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.

    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.


    • The minus sign in the result indicates a negative growth, or decay. To find the amount for any time period, multiply the time period by the decay rate and raise e, the natural logarithm base, to the power of the result. Then take that answer and multiply it by the initial value. For example, to find the bacteria population after 5 hours, multiply 5 by -0.111571776 to obtain -0.55785888. E to the power of -0.55785888 is 0.57243340. Multiply 0.57243340 by 100, the initial population, to get 57.243340 after 5 hours.

Related Articles

How to Write a Linear Decay Function
How to Calculate Rate of Decrease
How to Calculate Exponential Growth
How to Write a Linear Decay Function
How to Convert Pounds Per Square Foot to PSI
How to Calculate a T-Statistic
How to Find the Volume of a Sphere in Terms of Pi
How to Find a Fraction of a Number
How to Multiply and Divide Mixed Fractions
How to Calculate KVA to MVA
How to Convert Kilojoules to Kilocalories
How to Do Fractions on a TI-30X IIS
How to Divide Using Logarithms
How to Calculate Isotopes
How to Convert Seconds Into Miles Per Hour
How to Get a Remainder in Your Calculator
How to Change Improper Fractions to Mixed Numbers or...
How to Write an Equivalent Fraction With a Given Denominator
How to Find Partial Pressures
How to Find the X Intercept of a Function