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  2. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).

  3. Growth rate (group theory) - Wikipedia

    en.wikipedia.org/wiki/Growth_rate_(group_theory)

    In the mathematical subject of geometric group theory, the growth rate of a group with respect to a symmetric generating set describes how fast a group grows. Every element in the group can be written as a product of generators, and the growth rate counts the number of elements that can be written as a product of length n.

  4. 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 ...

  5. Gromov's theorem on groups of polynomial growth - Wikipedia

    en.wikipedia.org/wiki/Gromov's_theorem_on_groups...

    The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length at most n (relative to a symmetric generating set) is bounded above by a polynomial function p(n). The order of growth is then the least degree of any such polynomial ...

  6. Geometric mean - Wikipedia

    en.wikipedia.org/wiki/Geometric_mean

    The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...

  7. Population dynamics - Wikipedia

    en.wikipedia.org/wiki/Population_dynamics

    In logistic populations however, the intrinsic growth rate, also known as intrinsic rate of increase (r) is the relevant growth constant. Since generations of reproduction in a geometric population do not overlap (e.g. reproduce once a year) but do in an exponential population, geometric and exponential populations are usually considered to be ...

  8. Grigorchuk group - Wikipedia

    en.wikipedia.org/wiki/Grigorchuk_group

    The study of growth rates of finitely generated groups goes back to the 1950s and is motivated in part by the notion of volume entropy (that is, the growth rate of the volume of balls) in the universal covering space of a compact Riemannian manifold in differential geometry.

  9. Kelly criterion - Wikipedia

    en.wikipedia.org/wiki/Kelly_criterion

    In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate. John Larry Kelly Jr., a researcher at Bell Labs, described the criterion in ...