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  2. Bateman equation - Wikipedia

    en.wikipedia.org/wiki/Bateman_equation

    The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). Bateman found a general explicit formula for the amounts by taking the Laplace transform of the variables. (it can also be expanded with source terms, if ...

  3. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...

  4. Exponential decay - Wikipedia

    en.wikipedia.org/wiki/Exponential_decay

    Exponential decay. 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.

  5. Benford's law - Wikipedia

    en.wikipedia.org/wiki/Benford's_law

    This is an accepted version of this page This is the latest accepted revision, reviewed on 17 September 2024. Observation that in many real-life datasets, the leading digit is likely to be small Not to be confused with the unrelated adage Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the ...

  6. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = ⁡ or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

  7. Common logarithm - Wikipedia

    en.wikipedia.org/wiki/Common_logarithm

    An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [note 2] Thus, log tables need only show the fractional part. Tables of common ...

  8. Doubling time - Wikipedia

    en.wikipedia.org/wiki/Doubling_time

    The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life. As an example, Canada's net population growth was 2.7 percent in the year 2022, dividing 72 by 2.7 gives an approximate doubling time of about 27 years.

  9. Logarithmic growth - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_growth

    Logarithmic growth is the inverse of exponential growth and is very slow. [2] A familiar example of logarithmic growth is a number, N, in positional notation, which grows as log b (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic. [3] In more advanced mathematics, the partial sums of the harmonic series

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