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    1-028-SouthernSweetIcedTea-ModelingScenario
    We offer raw data collected from a webcam and a thermometer for evaluating the strength of steeping tea. We ask students to build a mathematical model using the data to predict how long the tea...

    Keywords: dataNewton's Law of Coolingteasweet tea

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    1-023-RumorSpread-ModelingScenario
    We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation.

    Keywords: Internetlogisticspreadrumors

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    1-011A-Kinetics-ModelingScenario
    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.

    Keywords: kineticsLaw of Mass Actionfittingorder of reactionchemical reaction

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    1-001s-StochasticMDeathImmigration-ModelingScenario
    We develop a mathematical model of a death and immigration process using m&ms as a stochastic process with the help of probability generating functions (pgf). We start with 50 m&ms in a bag.

    Keywords: simulationdatalogisticimmigrationstochasticdeathfitting

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    1-059-ContainerShapeFallingWater-ModelingScenario
    We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the...

    Keywords: containersTorricelli's Lawshapedischarge coefficient

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    1-060-SalesMarketing-ModelingScenario
    We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods...

    Keywords: marketingBass modelsalesconsumer productsinnovatorsimitators

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    1-061-PotatoCooling-ModelingScenario
    We model the cooling of a baked potato and compare it to student-collected data.

    Keywords: least sum of square errorsNewton's Law of Coolingcoolingpotato

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    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our...

    Keywords: concentrationSurface AreacolorNewton's Law of Coolingteasugar

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    1-101-ClassMMDeathImmigration-ModelingScenario
    We offer students an opportunity to generate unique data for their team on a death and immigration model using m&m's and then pass on the data to another student team for analysis with a model they...

    Keywords: simulationimmigrationdata collectiondeath

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including ...

    Keywords: optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy

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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and...

    Keywords: Lanchester's lawssensitivity analysisanalysis

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    1-141-MMGameRevisited-ModelingScenario
    It is assumed that the probability of an M&M chocolate, when tossed, falling on the M side is 0.5 The goal is to find a probability distribution of the probability q which is Pr(randomly chosen...

    Keywords: Probabilitystochastic processesBayesian methodsprobability distribution

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    1-142-WaterBottles-ModelingScenario
    This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or...

    Keywords: data collectionexperimenthalf-lifeNewton's Law of Coolingwater bottle

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    1-170-CensusModeling-ModelingScenario
    Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in...

    Keywords: logistic growthexponentialpopulationU.S. Census DataassumptionGoogle SheetsUnites StatesGuatemala

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    3-019-ShuttleCockFalling-ModelingScenario
    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and...

    Keywords: resistancegravityFree Body Diagramshuttlecockfallingc object

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    6-020-AlgaePopulationSelf-Replenishment-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A

    Keywords: algaepopulationMexicoqualitativecompartmentlinearizationJacobianlaknondimensionalizationpplane

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    6-023-DroneHeadingHome-ModelingScenario
    We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.

    Keywords: dronesoursuitflight pathchange of variables

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    6-067-LotkaVolterra-ModelingScenario
    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities...

    Keywords: time seriesdatacompetitionLotka-Volterramodel fittingpredictiongauseRexperimental

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    4-055-ShatterWineGlass-ModelingScenario
    This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?

    Keywords: frequencydampingamplituderesonanceoscillationshatteringwine glassbridgesaircraftexternal force

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    1-127-FishHarvesting-ModelingScenario
    We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not...

    Keywords: Management Of Dataoptimal controlfisherieslogisticharvestingmaximum sustainable yield

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