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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.
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.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. Learn about the three main types of decay (alpha, beta, and gamma), the discovery of radioactivity by Becquerel, Curie and others, and the early health dangers of X-rays.
Exponential smoothing or exponential moving average (EMA) is a technique for smoothing time series data using the exponential window function. Learn the basic formulas, applications, optimization and extensions of this method.
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.
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 compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal distribution. In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.
Alternatively, since the radioactive decay contributes to the "physical (i.e. radioactive)" half-life, while the metabolic elimination processes determines the "biological" half-life of the radionuclide, the two act as parallel paths for elimination of the radioactivity, the effective half-life could also be represented by the formula: [1] [2]