Um modelo matemático de crescimento e decaimento e algumas aplicações.

Abstract

This studyischaracterizedasabibliographicalresearch,whoseobjectiveistoexploreamathe- matical modelofgrowthanddecayappliedtosomeareasofscientificknowledge.Whenstudying the OrdinaryDifferentialEquationsubject,itwaspossibletostudysomeofitsapplications,from there camethequestioningofhowasamemathematicalmodelcanbeusedtosolveproblemsof differentnatures,thusarousingthecuriosityandmotivationforthiswork.Themodelpresented here canbeeasilysolved,howeverwhatmakesitinterestingisthatthroughit,onecaninterpret problems as:populationdynamics,intheareaofBiologicalSciences;radioactivedecay,inthe area ofChemistryandPhysics;continuouscapitalizationinFinancialMathematics;amongother applications. Atfirst,itwaspresentedabriefintroductionregardingmathematicalmodelingand the modelthatwillserveasabasisforsolvingtheproblemsanalyzed.Then,someconcepts and resultsonfirstorderlinearOrdinaryDifferentialEquationswerediscussed,emphasizing the resolutionofthemodel.However,wehaveexploredsomeproblemsthatstartfromdifferent concepts andrequirements,butthatadapttoacommonmodel,whosemathematicalsolution is equal,neverthelesscanhavetotallydifferentinterpretations,dependingonthevariablesand constants ofproportionalityofeachone.Throughthisresearch,wenotetheneedtostudy traditional models,sinceknowledgeacquiredinoneproblemcanbetransferredtoothers.