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    1-097-SwimmingPool-ModelingScenario
    This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.

    Keywords: concentrationcchlorinenumerical errorswimming poolhorineerreor

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    1-087-ThanosPopulationDynamics-ModelingScenario
    In the end of the “Avengers Infinity War,” the villain 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...

    Keywords: logisticexponentialpopulationThanos

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    1-023-RumorSpread-ModelingScenario
    We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation.

    Keywords: Internetlogisticspreadrumors

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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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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through...

    Keywords: Googleexponential growthlanguageword problemsetymologyNgrampropagationJumbo

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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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    1-040-OutcomeSavings-ModelingScenario
    We ask students to build a model for a savings account and to determine the monthly deposit in a savings account in order meet a long term savings goal.

    Keywords: Pop_Growth Pilotsavingsgrowthdepositg

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    1-047a-CondensationOptimization-ModelingScenario
    We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top...

    Keywords: simulationdataoptimizationenergycondensationbest fitcostsum of scquare errors

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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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    1-066-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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    1-067-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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    1-079-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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    1-081-TumorGrowth-ModelingScenario
    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor...

    Keywords: logisticpopulationtumorGompertz

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    1-100-EngineeringDemographics-ModelingScenario
    Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of...

    Keywords: logisticpopulationImproved Euler MethodGompertzdemographicswomenautonomous

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including ...

    Keywords: optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including...

    Keywords: optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz

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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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    1-118-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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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This...

    Keywords: population dynamicsdairyfarmers' marketsgrowthcow

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