title: [The function W = (a--b e-ct)n, a generalization of the classical growth functions (author's transl)].
abstract: The generalization of Bertalanffy's function of length and mass growth and the extension of the Gompertz function to 4 parameters as exercised by the author (Sager 1979 b, a) leads to the equation W = (a--b e-ct)n with positive values of n, and b in the first case and negative ones for n and b in the second case. It is shown that with the range of values for n the above expression comprises all classical functions of organic growth, namely the logistic or Verhulst function (1838), the Mitscherlich function (1919), and the Pütter-Bertalanffy functions (1920, 1934) of length and mass development. Moreover, the limiting case n leads to +/- infinity leads to the Gompertz-function (1825), as can be verified by the increase ansatz of the universal expression. Beside graphs examples are given showing the evaluation of the parameters a, b, c and n in the case of free choice as well as c, d and n for the transformed notation W = W0 [(1--de-ct)/(1--d)]n with a given initial value W0 leaving three parameters for choice.
mesh_terms: D000818:Animals; D000886:Anthropometry; D006128:Growth; D008433:Mathematics
vernacular_title: Die Funktion W = (a--b e-ct)n als verallgemeinerung der klassischen Wachstumsfunktionen.