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    1-034-T-FishMixing-ModelingScenario
    This activity gives students a chance to build the underlying differential equation and/or difference equation for a mixing problem using tangible objects (fish) and a student-designed restocking...

    Keywords: simulationfishFishingmixingrestocking

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    1-033-SouthernBarbeque-ModelingScenario
    We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the...

    Keywords: nonlinear regressionlogisticNewton's Law of Cooling-Warmingbarbecue

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    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.

    Keywords: population dynamicsmalariaPolicyDecision-makingEuler's methodpharmacokineticsmosquitoimproved Euler's methodHuen's methodUS Army

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    1-021-FeralCatControl-ModelingScenario
    Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of...

    Keywords: population growthcontrolferal catspopulation controlneutertrap-killtrap-neuter-return

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    1-017-DiseaseSpread-ModelingScenario
    Using a grid and m&m candies, we simulate the spread of disease. Students conduct the simulation and collect data to estimate parameters (in several ways) in a differential equation model for the...
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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.

    Keywords: projectile motionaccelerationNewton's Law of Coolingspeeding

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    1-039-StochasticPopModels-ModelingScenario
    We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is...

    Keywords: Probabilitypopulation dynamicsVarianceMeanstochasticdeterministic

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    1-045-TimeOfDeath-ModelingScenario
    Students are asked to determine the time of death given both environmental temperature situations and two observations of body temperature under several different circumstances.

    Keywords: body masstemperaturedeathNewton's Law of Coolingbody temperature

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    1-062-BacteriaGrowth-ModelingScenario
    We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential...

    Keywords: bacteriaexponentialgrowth

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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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    1-067-ModelingWithSigmoidCurves-ModelingScenario
    The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the...

    Keywords: logisticGompertzsigmoidVerhulst-Pearl

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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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    1-104-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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    1-130-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.

    Keywords: pharmacokineticsdrugaspirin

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    1-135-FishHarvesting-ModelingScenario
    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the...

    Keywords: population dynamicsfishstabilitybifurcationharvest

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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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    3-087-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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    5-022-ColdPill-ModelingScenario
    A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation...

    Keywords: ratesmedicinedrug discoverycompartmentcold pillgastrointestinalbloodstream

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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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    6-018-ExploringSIRModel-ModelingScenario
    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to...

    Keywords: population dynamicssensitivitydiseaseSIR modelsepidemicrumors

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