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    Modeling Scenario
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    1-131-CaffeineElimination-ModelingScenario
    We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    caffeineeliminationpharmacokineticsdrug
    Modeling Scenario
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    1-078-MonodGrowthModel-ModelingScenario
    Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
    bacterianutrient cyclesgrowthMonodconsumption
    Modeling Scenario
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    1-031-CoolIt-ModelingScenario
    We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
    SpanishNewton's Law of Coolingcooling
    Modeling Scenario
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    5-007-ChemOpt-ModelingScenario
    Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
    optimizationpYield and sustainabilitynonprofit managementLaw of Mass Actionkineticreaction
    Modeling Scenario
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    3-034-CarSuspension-ModelingScenario
    We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.
    designspring-mass-dashpotspring constantunderdampingcar suspensionsuspension tolerancestatic equilibrium
    Modeling Scenario
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    1-026-Evaporation-ModelingScenario
    We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
    evaporationconealcoholPetri dish
    Article or Presentation
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    510

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    2020-TeachingModule-ModelingNonlethalInfluenzaEpidemic
    We discuss the modeling efforts and tools for success in modeling the spread of nonlethal influenza in an English boarding school
    moduleepidemicboarding schoolTeaching Module
    Article or Presentation
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    570

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    2020-TeachingModule-ModelingSpreadOfOilSlick
    This is support material and video for teaching a Modeling Scenario using a first order ODE to model the spread of an oilslick with incomplete data.
    moduleoil slickTeaching Module
    Modeling Scenario
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    1-132-DigoxinElimination-ModelingScenario
    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    nullclinespharmacokineticsdigoxindrug eliminationtwo compartment
    Modeling Scenario
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    324

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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.
    dataphysicsdynamicsdata collectionrollingslippingripcordtoy
    Modeling Scenario
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    178

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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
    gravityinverse problemacceleration
    Modeling Scenario
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    1-015-Torricelli-ModelingScenario
    We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
    dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver
    Technique Narrative
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    242

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    1-015-DimensionlessVariables-TechniqueNarrative
    This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
    linearizationdimensional analysistime scalescalingdimensionless variablesspatial scale
    Modeling Scenario
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    182

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    1-025-MixingItUp-ModelingScenario
    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.
    compartmentsalttankmixing
    Modeling Scenario
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    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
    exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano
    Modeling Scenario
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    3-103-PullBackCars-ModelingScenario
    This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
    modelingdynamicshands-ontoypull-back carpullback
    Modeling Scenario
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    6-070-BeerBubbles-ModelingScenario
    The goal of this project is to set up and numerically solve a first-order nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top.
    molecular forensicsBEERspherebubbleNewton' Second LawIdeal Gas Lawdrag forceHadamardStokesmole
    Modeling Scenario
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    6-004-VillageEpidemic-ModelingScenario
    Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.
    SIR modelsepidemicsusceptibleinfectiveremovedEyamEnglish village
    Modeling Scenario
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    1-001-MM-DeathAndImmigration-ModelingScenario
    We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!
    simulationimmigrationdeathSpanishdatsWinkelBrian Winkel
    Modeling Scenario
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    1-038-Ebola-ModelingScenario
    Students will use data published by the World Health Organization to model the 2014 outbreak of the Ebola virus in West Africa. We begin with a simple exponential growth model and move through the modeling process to the logistic growth model.
    population dynamicsdata analysisexponential growthEbolalogisticepidemic