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Exponential decay is a process where a quantity decreases at a rate proportional to its current value. Learn the differential equation, the decay constant, the mean lifetime, the half-life, and the applications of exponential decay in physics, chemistry, biology, and more.
Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the rate of change is proportional to the quantity itself. See examples, formula, and applications in biology, physics, economics, finance, and computer science.
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.
The time constant, denoted by τ, is a parameter that characterizes the response of a first-order, linear time-invariant system to a step input. Learn how to calculate the time constant, its relation to the bandwidth, and its applications in physics, engineering and radioactive decay.
A power law is a functional relationship between two quantities that varies as a power of each other. Learn about the empirical examples, properties, and scientific interest in power laws, such as the Pareto distribution, fractals, and universality classes.
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 ...
Particle decay is the spontaneous transformation of an unstable subatomic particle into multiple other particles. Learn how to calculate the decay rate, the probability of survival and the complex mass of a particle, and see some examples of particle decays.