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  2. 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 ...

  3. 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.

  4. Exponential distribution - Wikipedia

    en.wikipedia.org/wiki/Exponential_distribution

    In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...

  5. Malthusian growth model - Wikipedia

    en.wikipedia.org/wiki/Malthusian_growth_model

    A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most ...

  6. Log–log plot - Wikipedia

    en.wikipedia.org/wiki/Log–log_plot

    Comparison of Linear, Concave, and Convex Functions In original (left) and log10 (right) scales. In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight ...

  7. Proof that e is irrational - Wikipedia

    en.wikipedia.org/wiki/Proof_that_e_is_irrational

    Use the assumption that e = a b to obtain. The first term is an integer, and every fraction in the sum is actually an integer because n ≤ b for each term. Therefore, under the assumption that e is rational, x is an integer. We now prove that 0 < x < 1. First, to prove that x is strictly positive, we insert the above series representation of e ...

  8. Leslie matrix - Wikipedia

    en.wikipedia.org/wiki/Leslie_matrix

    The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. The Leslie matrix (also called the Leslie model) is one of the most well-known ways to describe the growth of populations (and their projected age distribution), in which a population is closed to migration, growing in an unlimited environment ...

  9. Biological exponential growth - Wikipedia

    en.wikipedia.org/wiki/Biological_exponential_growth

    Biological exponential growth. Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. 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 ...

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