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Learn about the mathematical model of exponential decay, which describes how a quantity decreases at a constant rate proportional to its current value. Find out how to calculate the decay constant, mean lifetime, half-life, and other related concepts, and see examples of exponential decay in physics, chemistry, biology, and other fields.
Time constant (τ) is a parameter that characterizes the response of a first-order, linear time-invariant system to a step input. Learn how to calculate and interpret the time constant, its relation to bandwidth, and its applications in physics, engineering and radioactive decay.
Half-life is the time required for a quantity to reduce to half of its initial value. Learn how to calculate half-life for different types of exponential decay, such as radioactive decay, chemical reactions and population growth, with formulas and examples.
Exponential growth is a process that increases quantity over time at an ever-increasing rate. Learn the formula, the graph, and the applications of exponential growth in biology, physics, economics, finance, computer science, and internet phenomena.
Doubling time is the time it takes for a population to double in size or value. Learn how to calculate it from the growth rate, and see examples of doubling times for various phenomena such as population, inflation, interest and tumours.
The plateau principle is a model that describes the time course of change in a system with constant input and output. It applies to drug action, nutrition, biochemistry, and system dynamics. Learn the equations, examples, and applications of the plateau principle.
In phenomenological applications, it is often not clear whether the stretched exponential function should be used to describe the differential or the integral distribution function—or neither. In each case, one gets the same asymptotic decay, but a different power law prefactor, which makes fits more ambiguous than for simple exponentials.
The term e-folding time is also sometimes used similarly in the case of exponential decay, to refer to the timescale for a quantity to decrease to 1/e of its previous value. The process of evolving to equilibrium is often characterized by a time scale called the e-folding time, τ. This time is used for processes which evolve exponentially ...