According to Weil (2009) one of the stylized facts of the international economic growth is a positive association between savings rates and per capita income levels. This paper proposes a new interpretation of this fact by a Solow-type model but expanded with a hypothesis of a positive influence of the capital on the savings rate. The model thus amended, a "quasi-Solow" model, can generate the case of "endogenous growth" or the case of exogenous growth, either case depending on the specific value that takes a parameter of the savings rate function. The main conclusion is this: a model of economic growth which, in essence, is a "solownian" one, as the model described in these pages, may be useful to interpret a process of economic growth through the very long time.