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    1-063-ThreeHoleColumnOfWater-ModelingScenario
    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

    Keywords: fallingcolumn of waterTorricelli's Lawmultiple spigotsspigots

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    1-065-AlgalBlooms-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.

    Keywords: direction fieldstool:dfieldalgaeharmful algae bloomspopulationcompartmentLake Chapala

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    1-066-USCensusModeling-ModelingScenario
    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.

    Keywords: datalogisticpopulationGompertzcensusgoodness of fit

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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.

    Keywords: bNewton's Law of Coolingwater bottleautonomousbottle

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    1-079-HomeHeating-ModelingScenario
    This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature...

    Keywords: Optimal Control TheorytemperatureheatfurnaceNewton's Law of Coolinghome heatingspecific heat

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    1-088-RoomTemperature-ModelingScenario
    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume...

    Keywords: environmentclimatetemperatureNewton's Law of Coolingcoolingperiodic function

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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...

    Keywords: VolumesphereTorricelli's Lawtimingspherical tankfluidempty

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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss...

    Keywords: slope fieldspopulation

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    1-093-SucroseReaction-ModelingScenario
    We offer data on the hydrolysis of sucrose in the presence of catalyst sucrase. We present students with several models and ask which model is best. We ask students to estimate parameters for the...

    Keywords: kineticsMichaelis-Mentenhydrolysisreactionsucrose

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    1-104-InfectionRisk-ModelingScenario
    This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.

    Keywords: infectionlogisticexponentialcovidcarrying capacity

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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface...

    Keywords: climateenergytemperaturelinearizationphase linesenergy balance modelroot finding

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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a...

    Keywords: optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth

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    1-134-LanguageDynamics-ModelingScenario
    Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another.

    Keywords: languagecompartmentphase linesbifurcationswitching

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    3-026-SpringInverseProblem-ModelingScenario
    We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.

    Keywords: datamassinverse problemspring\parameter estimate

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    3-072-EarthQuakePartI-ModelingScenario
    This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.

    Keywords: earthquakevibrationamplituderesonanceundampedspring-mass system

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    3-075-RLCCircuits-ModelingScenario
    We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

    Keywords: resistancecircuitvoltageinductancecapacitancecurrentKirchhoff's Law

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    3-087-ThanosPopulationDynamicsInteractingSpecies-ModelingScenario
    Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species?

    Keywords: species interactionspredator-preycompetitionLotka-Volterrasensitivity analysisdynamicspopulation

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    4-020-AnIEDBlast-ModelingScenario
    These three exercises offer students a chance to model with second order ordinary differential equations, how they might incorporate a spring-mass system into a larger model, and how they can use...

    Keywords: applied mathematicsforcesFree Body DiagramImprovised Explosive Devicessum of forces

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    5-014-TwoSpringMass-ModelingScenario
    We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join...

    Keywords: massspring mass dampersprings

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    6-010-SocialCampaign-ModelingScenario
    The epidemic modeling problem is formulated as a system of three nonlinear, first order differential equations in which three compartments (S, I, and R) of the population are linked.

    Keywords: diseasegrowth rateJudgment and Decision MakingSIR modelinfections diseasesocial campaignrecovery ratedelay timejoining processquitting processexponential distribution

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