It is not uncommon to find situations in which on is asked to make both lony and short term predictions for a particular phenomena, without having at this or her disposal the necessary information concerning the factors which might be directly affecting the phenomena ins question. Given this state of affairs, the use of mathematical functions in modelling becomes justified. Our aim in this thesis in to model monotonically growing phenomena which present an asymptotic limit. The mathematical functions entertained here are those know as growing functions with as S shape . In particular 8 shape. In particular we focus our attention on those function from the generalized modified exponential family. The formulations we exploit are the statistic, the dynamic classic and the Bayesian dynamic with discount factors. We apply the aforementioned methodologies to six time series: the number of AIDS cases in Brazil, the percentage of USA homes with a telephone, the percentage of USA homes with a wirelesss telephone, the percentage of fabrics manufactured in the USA as compared to the total USA market, the stock of tractors in Spain and the percentage of USA homes with a monochromatic TV set.