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    Modeling Scenario
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    1-085-DrugBolus-ModelingScenario
    Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?
    concentrationsum of square errorsbolusdrugrate constantadminister
    Modeling Scenario
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    1-058-WaterClocks-ModelingScenario
    We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.
    flowTorricelli's Lawspigotswater clock
    Modeling Scenario
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    1-130-AspirinAbsorption-ModelingScenario
    We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    pharmacokineticsdrugaspirin
    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
    Modeling Scenario
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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.
    population dynamicshumangrowth ratevarying growth rate
    Modeling Scenario
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    1-090-EmptySphericalTank-ModelingScenario
    We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
    VolumesphereTorricelli's Lawtimingspherical tankfluidempty
    Modeling Scenario
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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 choosing which model to use.
    logistic growthexponentialpopulationU.S. Census DataassumptionGoogle SheetsUnites StatesGuatemala
    Modeling Scenario
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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.
    kineticsLaw of Mass Actionfittingorder of reactionchemical reaction
    Modeling Scenario
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    1-140-LeakyBucket-ModelingScenario
    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.
    flowTorricelli's Lawleaky bucket
    Modeling Scenario
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    1-080-DrugAdministration-ModelingScenario
    A simple drug administration situation is modeled with only two observations.
    decaybloodstreamdrugrate constantadminister
    Modeling Scenario
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    1-128-RocketFlight-ModelingScenario
    We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...
    resistanceFlightRocketrymassNewton's Second Law of MotionthrustFree Body Diagramapexrocket
    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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    5-030-AirshedSulphur-ModelingScenario
    Temperature inversions and low wind speeds trap air pollutants in a mountain valley for a period of time. Gaseous sulfur compounds are a significant air pollution problem. We offer a model for analysis to predict long-term levels of levels of...
    sulphurpollutionairshedhydrogen sulfidesulfur dioxide
    Modeling Scenario
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    1-005A-ChemDataCollection-ModelingScenario
    A student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting data. She only collects data at the start and end of a number of ten minute intervals and does not keep track of when the observations are...
    linear regressionkineticschemistryorder of reactionchemical reactionchemical datainfusiondifferencing
    Modeling Scenario
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    3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.
    massundampedFree Body Diagramspringstwo springsoscillationspring constantfixed ends
    Modeling Scenario
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    4-036-AltitudeDependentGravity-ModelingScenario
    When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
    agravityprojectilelinearizationltitufealtitude
    Modeling Scenario
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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
    undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation
    Modeling Scenario
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    7-040-TankInterruptMixing-ModelingScenario
    We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.
    Laplace transforminverse Laplace Transformsalttankmixinginterrupt
    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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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
    projectile motionaccelerationNewton's Law of Coolingspeeding