Population dynamics is analyzed by means of the power series expansion of a decay ratio F(P) with respect to the continuation probability, P, of survival. The truncation of the higher terms of the series yields the Verhulst equation as a first approximation. The approximation for higher age yields a simple exponential decay law of population, while the younger-age approximation recovers Gompertz's empirical law of human mortality. It is shown that there exists a finite survival probability in the limit of t = infinity. The validity of the present result is examined with real population dynamics of centenarians. In order to construct a commensurable definition of aging, an aging phenomenon in decay process is considered on the assumption of an ideal society, from which a simple relationship is derived between the extent of advancement of aging and the continuation probability.