A four-parameter generalization of the logistic curve is proposed for the description of population growth and decline. Limiting cases of this new model include logistic and exponential growth and decline. Unlike an earlier generalization, which is monotonic, the present asymptotic curve declines after reaching a single maximum. In studies of natural populations, where many factors are interacting and where population growth may initially have beneficial effects, the present model may be more widely applicable than more complicated and restrictive theoretical models. The fitting of the present curve and of the corresponding log-normal variation belts through multiplicative iteratively-reweighted least squares is illustrated on data about an experimental population of Paramecium caudatum and about the seasonal change in the numbers of captures of male Meromyza variegata. This model could be applied also to populations of molecules or cells within individual organisms.