Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Abstract

Growth functions with upper horizontal asymptote do not have a maximum point, but we frequently question from which point growth can be considered practically constant, that is, from which point the curve is sufficiently close to its asymptote, so that the difference can be considered non-significant. Several methods have been employed for this purpose, such as one that verifies the significance of the difference between the curve and its asymptote using a t-test, and that of Portz et al. (2000), who used segmented regression. In the present work, we used logistic growth function, which has horizontal asymptote and one inflection point, and applied a new method consisting in the mathematical determination of a point in the curve from which the growth acceleration asymptotically tends to zero. This method showed the advantage to have biological meaning besides leading to a point quite close to those obtained using the beforementioned methods.