A Study Over Determination of Asymptotic Deceleration and Absolute Acceleration Points in Logistic Growth Model

Abstract

Since growth models has generally upper horizontal asymptote, they do not have a maximum point. We wonder about after which point growth can be considered constant, that is, after which point the curve of the growth function is too close to its asymptote. That point is called maximum deceleration point. After this point the deceleration is very slow and the second derivative of the growth function goes to zero as time tends to infinity. After this point it is considered that the amount of the growth is quite small. Moreover, we wonder about which point is an absolute acceleration point so that before that point acceleration is very slow and after that point actual acceleration starts. So we could say that after this point actual growth starts. In this study, the logistic growth model was used to investigate these points, asymptotic deceleration and absolute acceleration points in addition to the other critical and important points such as inflection point, maximum acceleration point, maximum deceleration point. The graphs of the logistic growth model which show all these points mentioned above are also given by using a data set.

Keywords

• Logistic model,asymptotic deceleration point,absolute acceleration point,inflection point

References

1. Chatkin, J. M., Fiterman, J., Fonseca, N.A., Fritscher, C.C. 2001. Change in asthma mortality trends in children and adolescents in Rio Grande do Sul: 1970–1998, Jornal de Pneumologia 27, (2001), 89–93. (in Portuguese, with abstract in English).
2. Gregorczyk, A., Richards plant growth model, Journal of Agronomy and Crop Science 181 (1998), 243–247.
3. Mischan, M.M., Pinho, S.Z., Carvalho, L.R., Determination of a point su_ciently close to the asymptote in nonlinear growth functions, Scientia Agricola. (Piracicaba, Braz.) 68(1), (2011),109–114.
4. Yıldızbakan, A., Analysis on mathematical models of tree growth and comparison of these models, MSc Thesis, Institute of Natural and Applied Sciences, University of Cukurova, Turkey, 2005 (in Turkish, with abstract in English).