A simple but flexible growth function

The functional form W(t) = Wf - (Wf - Wo) exp[-k infinite (t - T) + 2c(root of t - root of T)] where Wf, Wo, k infinite, c and T are constants, is derived as a growth equation and evaluated using commonly applied growth functions such as the Gompertz, logistic, monomolecular and Richards. Further evaluation is made with reference to sets of observations on growth in a number of animal species ranging from mice to horses. The new function provides a flexible growth equation capable of describing sigmoidal and diminishing returns behaviour. It appears adept at describing sigmoidal patterns exhibiting faster early growth and a fairly low but variable point of inflexion, and can therefore be perceived as a generalised Gompertz equation. The function also has the ability to describe a wide range of hyperbolic shapes when there is no point of inflexion. The analysis described suggests that this simple equation is a worthwhile addition to the corpus of growth functions.