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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon....

    Keywords: compartmentsalttankmixingflow

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    1-054-GrowthInFarmland-ModelingScenario
    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model,...

    Keywords: fittingfarmfarmland

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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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    1-080-DrugAdministration-ModelingScenario
    A simple drug administration situation is modeled with only two observations.

    Keywords: decaybloodstreamdrugrate constantadminister

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    1-083-FallingMeteorites-ModelingScenario
    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a...

    Keywords: falling objectdragvariable massfactor rankingmeteormeteorite

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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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    1-091-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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    1-104-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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    1-138-InnerEarDrugDelivery-ModelingScenario
    Students examine local drug delivery to the cochlea. The delivery system is modeled as a liquid mixing problem. Students formulate the differential equation, and solve the equation using separation...

    Keywords: concentrationdrug deliveryinner earcochleahearing loss

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    1-143-PopulationModelVariationsMATLAB-ModelingScenario
    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.

    Keywords: population dynamicsecologylogistic growthbifurcation theoryslope fieldsextinctionharvestingqualitative analysisstocking

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    3-009-BallDropInWater-ModelingScenario
    We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal...

    Keywords: resistancegravityfalling bodyterminal velocitybuoyancy

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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring...

    Keywords: energymass-spring systemkinetic energypotential energytotal energy

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    3-013-WhiffleBallFall-ModelingScenario
    We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models.

    Keywords: Akaike Information CriterionresistancegravityFree Body Diagramforcefalling objectWhiffle ball

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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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    3-031-SpringCost-ModelingScenario
    We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and...

    Keywords: designunit costspring constantstatic equilibriumspring masss dashpot

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    3-035-StadiumDesign-ModelingScenario
    For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?

    Keywords: projectile motionbaseballparametric equationstadiumhome runno reistantfairnessno resistance

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    3-041-UpDown-ModelingScenario
    Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and...

    Keywords: gravityprojectile motionfalling bodymaximum heightftiming

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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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