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  2. Wheat and chessboard problem - Wikipedia

    en.wikipedia.org/wiki/Wheat_and_chessboard_problem

    The exercise of working through this problem may be used to explain and demonstrate exponents and the quick growth of exponential and geometric sequences. It can also be used to illustrate sigma notation. When expressed as exponents, the geometric series is: 2 0 + 2 1 + 2 2 + 2 3 + ... and so forth, up to 2 63. The base of each exponentiation ...

  3. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function () = grows at an ever increasing rate, but is much slower than growing

  4. Combinatorial explosion - Wikipedia

    en.wikipedia.org/wiki/Combinatorial_explosion

    (This growth is often casually described as "exponential" but is actually polynomial.) If two organizations need to communicate about a particular topic, it may be easiest to communicate directly in an ad hoc manner—only one channel of communication is required. However, if a third organization is added, three separate channels are required.

  5. 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.

  6. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    However, if some elements of {α} or {β} are not zero, then function S has multitudes of additional singularities and cutlines in the complex plane, due to the exponential growth of sin and cos along the imaginary axis; the smaller the coefficients {α} and {β} are, the further away these singularities are from the real axis.

  7. Technological singularity - Wikipedia

    en.wikipedia.org/wiki/Technological_singularity

    For example, we could mistakenly elevate a subgoal to the status of a supergoal. We tell it to solve a mathematical problem, and it complies by turning all the matter in the solar system into a giant calculating device, in the process killing the person who asked the question.

  8. Malthusian growth model - Wikipedia

    en.wikipedia.org/wiki/Malthusian_growth_model

    By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. [8] Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:

  9. Double exponential function - Wikipedia

    en.wikipedia.org/wiki/Double_exponential_function

    An example of a problem in 2-EXPTIME that is not in EXPTIME is the problem of proving or disproving statements in Presburger arithmetic. [4] In some other problems in the design and analysis of algorithms, double exponential sequences are used within the design of an algorithm rather than in its analysis.

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