In this paper, an analytic approximation for Volterra's model for population growth of a species in a closed system is presented. The nonlinear integro-differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation. The decomposition algorithm are implemented independently to a related ODE. The Pade approximants, that often show superior performance over series approximations, are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals.
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