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Unformatted text preview: Notes for Day : . : Popu ation Dynamics In this section, we cover two more applications that can be modeled using rst-order linear equations. Popu ation Mode s Population models are similar to mixing models, which we covered in section . : In the mixing model, we measured the quantity of a substance owing in and out of the system, basing our di erential equation on the fact that the rate of change in that quantity was equal to the rate at which the substance owed in, minus the rate at which the substance owed out. Population models are similar, in that the rate of change in the population equals the birth rate r b minus the death rate r d . (If you think of people as a substance owing in and out of the population, you see how similar these models are!) In addition, there may be other types of population change due to migration in or out of the population. Population models have an additional source of potential error that mixing models do not: In real life, population can never be a fraction! (We say that population is anever be a fraction!...
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