In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line analysis, graphing approximate solutions) to analyse their models. We then discuss how to use aspects of a species' behaviour to choose an appropriate model from among the ones developed. Finally, we show how a professor could apply what students have learned to develop general principles for sustainable harvesting of such species.