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  2. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

  3. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth.

  4. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    The limit that defines the exponential function converges for every complex value of x, and therefore it can be used to extend the definition of ⁡ (), and thus , from the real numbers to any complex argument z. This extended exponential function still satisfies the exponential identity, and is commonly used for defining exponentiation for ...

  5. Characterizations of the exponential function - Wikipedia

    en.wikipedia.org/wiki/Characterizations_of_the...

    In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]

  6. Exponential field - Wikipedia

    en.wikipedia.org/wiki/Exponential_field

    One such function is the usual exponential function, that is E(x) = e x, since we have e x+y = e x e y and e 0 = 1, as required. Considering the ordered field R equipped with this function gives the ordered real exponential field, denoted R exp = (R, +, ·, <, 0, 1, exp).

  7. Malthusian growth model - Wikipedia

    en.wikipedia.org/wiki/Malthusian_growth_model

    Logistic function for the mathematical model used in Population dynamics that adjusts growth rate based on how close it is to the maximum a system can support; Albert Allen Bartlett – a leading proponent of the Malthusian Growth Model; Exogenous growth model – related growth model from economics; Growth theory – related ideas from economics

  8. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula states that, for any real number x, one has = ⁡ + ⁡, where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine").

  9. Tarski's exponential function problem - Wikipedia

    en.wikipedia.org/wiki/Tarski's_exponential...

    The problem can be reduced to finding an effective procedure for determining whether any given exponential polynomial in variables and with coefficients in has a solution in . Macintyre & Wilkie (1996) showed that Schanuel's conjecture implies such a procedure exists, and hence gave a conditional solution to Tarski's problem. [ 2 ]