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A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening.
Exponent bias; Exponential (disambiguation) Exponential backoff; Exponential decay; Exponential dichotomy; Exponential discounting; Exponential diophantine equation; Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function ...
Exponential growth or exponential decay—where the varaible change is proportional to the variable value—are thus modeled with exponential functions. Examples are unlimited population growth leading to Malthusian catastrophe , continuously compounded interest , and radioactive decay .
Parameters (negative in the case of exponential decay): The growth constant k is the frequency (number of times per unit time) of growing by a factor e ; in finance it is also called the logarithmic return, continuously compounded return , or force of interest .
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
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