Mathematical ReportStage 2 - Mathematical ModelsYour NameDateYear of StudyINTRODUCTIONThe report mainly focuses upon theoretical and practical applications of two wellknown mathematical models namely - Surge Functions, and Logistic Functions. Thereports initial section would be dealing with Surge models, and the later sectionwould be dealing with Logistic models. The two models have a wide range of realworld applications, and thus have found a place in the mathematical curriculum. ASurge function is mostly used to model system behaviours when the response to anaction rapidly increases during the initial phase and then decreases slowly in the laterphase. The Logistic function is used to model system behaviours when the rate ofgrowth changes from an increasing growth rate to a decreasing growth rate.THE SURGE FUNCTIONThe Surge function is in the form of () = ; > 0 , > 0. Surge modelsare used to measure response to a dose of drug, or a bodys response to an infection.A more general way of representing a surge function is () = ; >0 , > 0 , > 0. In this case we would be dealing with the case where = 1. Tobegin with graphing the Surge function, let us first fix the values of the constants.Let = 10 , = 4. The equation of the graph is hence - () = 10 4 .Calculating the derivative of the function = () ...
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