How to Find Exponential Rates
Exponential functions can represent the effects of compounding over time. Exponential functions are used to represent population growth and the increase in an investment's value over time. In order to calculate exponential growth rate functions, you need to know the amount you are starting with, the growth rate per time period and the number of time periods the growth occurs over. People often use years for time periods, because growth rates are often measured per year. However, you can use any time period including months, days or seconds.
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Instructions
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1
Determine the rate of growth. For example, if you want to determine how much your retirement account will be worth in the future, you could estimate the rate of growth at 7 percent.
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2
Convert the percentage to a decimal by dividing by 100. For example, 7 percent would become 0.07.
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3
Add 1 to the growth rate expressed as a decimal. For example, 0.07 would become 1.07.
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4
Raise the result from step 4 to the nth power, where n is the number of time periods the growth will occur over. For example, if you are expecting a 7 percent growth rate per year for 20 years, use 20 for the number of time periods so you would raise 1.07 to the 20th power and get about 3.8697.
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5
Multiply the result from step 4 by the initial amount. For example, if you started with $20,000 in your account, multiply it by 3.8697 and find that if your account grew at 7 percent per year for 20 years it would be worth $77,394.
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Tips & Warnings
If you want to calculate an exponential decay, such as a loss of 5 percent per year, you would subtract the rate from 1 rather than adding one in step 3.
