A broad class of normal and non-normal models for processes with non-n
egative and non-decreasing mean function is presented. This class is c
alled exponential growth models and the inferential procedure is based
on dynamic Bayesian forecasting techniques. The aim is to produce the
analysis on the original variable avoiding transformation and giving
to the practitioner the opportunity to communicate easily with the mod
el. This class of models includes the well-known exponential, logistic
and Gompertz models. Models for counting data are compared with the N
ormal models using the appropriate variance law. In the examples, the
novel aspects of this class of models are illustrated showing an impro
ved performance over simple, standard linear models.