Exponential decay calculator
Exponential decay is exponential growth with a negative rate, and its half-life is fixed whatever the starting amount.
%
Final value
121.576 654 591
- Amount lost
- 878.423 345 409
- Share remaining
- 12.1577 %
- Half-life in periods
- 6.5788
- Decay constant
- 0.105 360 52
Show the working
- Starting value = 1000
- Decay rate per period = 10
- Periods = 20
- factor = 1 - 10/100 = 0.9
- Final value = 1000 * 0.9^20 = 121.577
- Amount lost = 1000 - 121.577 = 878.423
- Half-life in periods = 10 > 0 ? log(0.5, 0.9) : 0 = 6.578 81
- Decay constant = 0.9 > 0 ? -ln(0.9) : 0 = 0.105 361
- Share remaining = 1000 != 0 ? 121.577/1000*100 : 0 = 12.1577
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- N = N0 (1 - r)^t
- half-life = ln(0.5) / ln(1 - r)