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A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [1] and the analytical solution was provided by Harry Bateman in 1910. [2]
the equation indicates that the decay constant λ has units of t −1, and can thus also be represented as 1/ τ, where τ is a characteristic time of the process called the time constant. In a radioactive decay process, this time constant is also the mean lifetime for decaying atoms.
A value of = indicates that the failure rate is constant over time. This might suggest random external events are causing mortality, or failure. The Weibull distribution reduces to an exponential distribution; A value of > indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more ...
If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression.
The decay correct might be used this way: a group of 20 animals is injected with a compound of interest on a Monday at 10:00 a.m. The compound is chemically joined to the isotope copper-64, which has a known half-life of 12.7 hours, or 764 minutes.
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period.