A generalization of the logistic equation of population biology is considered in which the species being modeled is connected to its larger ecosystem through a lower trophic level consisting of a renewable resource. The resource adjusts rapidly to demand and is utilized by the species for population growth. The resulting initial value problem is a system of first-order differential equations with a small parameter. Singular perturbation techniques based on different time scales are used to obtain and relate approximations valid initially and for order one times. A comparison of composite approximations with numerical solutions shows that, even for moderate values of the parameter, the asymptotic results are highly accurate. Additional situations studied include a model for long term species adaptation which involves three distinct time scales.