Work out how a value grows or shrinks exponentially over several periods, based on a starting value and growth rate.
Exponential growth happens when a value changes by a fixed percentage per period, instead of a fixed amount:
This formula is used for everything from bacterial growth and population growth to radioactive decay — just use a negative growth rate to model decay or decline. Compound interest is actually a special case of this same general formula, where the "period" is one year (or one compounding term).
Enter the starting amount, and use a negative growth rate corresponding to the decay rate per period. The final value then shows how much is left after the given number of periods.
Linear growth adds the same fixed amount every period, while exponential growth multiplies by a fixed factor every period. Exponential growth often starts slowly but accelerates quickly over time.
Yes. A negative growth rate gives exponential decay (decline) instead of growth — useful for modeling things like radioactive decay, depreciation of value, or a shrinking population.