Exponential decay

Exponential decay is a decrease in which the rate of change is proportional to the quantity remaining, producing a constant fractional decrease over equal time intervals.

Exponential function: A function whose value changes in proportion to itself, commonly written as an exponential of its input. Decay follows this function when the proportional rate is constant.
Radioactive decay: The spontaneous transformation of unstable atomic nuclei into other nuclei or particles. A large population of identical radioactive nuclei decays exponentially.
Linear decay: A decrease by a constant absolute amount per unit time. Unlike exponential decay, its rate does not depend on the amount remaining.
Rate constant: A parameter that sets the speed of a specified rate process. Its value determines how quickly the decaying quantity falls.
Differential equation: An equation relating an unknown function to one or more of its derivatives. The defining proportional-rate rule is expressed as a differential equation.
Pharmacokinetics: The study of how an organism absorbs, distributes, metabolizes, and eliminates substances. First-order drug elimination makes concentration fall exponentially over time.
Power law: A relation in which one quantity varies as a fixed power of another. Power-law decreases often have heavier tails than exponential decay.
Natural logarithm: The logarithm to base e, inverse to the natural exponential function. Taking logarithms turns an exponential decay curve into a straight line.
Exponential decay law: The relation stating that a quantity decreases exponentially when its rate of loss is proportional to its current amount. It states the governing rule in explicit mathematical form.
Newton's law of cooling: A model in which an object's temperature changes at a rate proportional to its difference from ambient temperature. It predicts exponential decay of the temperature difference under steady conditions.

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