
1067SModelingWithSigmoidCurves
18 Aug 2018  Modeling Scenarios  Contributor(s):: Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1032SDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1131SCaffeineElimination
15 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a reaction in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations, and it can be...

1130SAspirinAbsorption
15 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zeroorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

1089SSpreadOfDisease
15 Aug 2018  Modeling Scenarios  Contributor(s):: Shinemin Lin
In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

1054SGrowthInFarmland
14 Aug 2018  Modeling Scenarios  Contributor(s):: Richard Spindler
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, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

6007SFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s):: Meredith Greer

5026SEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s):: Mary Vanderschoot

1102SCancerGrowth
29 Jul 2018  Modeling Scenarios  Contributor(s):: Jue Wang
This scenario 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 exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...

1081STumorGrowth
09 Jun 2018  Modeling Scenarios  Contributor(s):: Ryan Miller, Randy Boucher
Students will transform, solve, and interpret a tumor growth scenario using nonlinear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

6018SExploringSIRModel
30 May 2018  Modeling Scenarios  Contributor(s):: Stanley Florkowski, Ryan Miller
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 understand, to apply, and to develop SIR models. Part one focuses on understanding and interpreting SIR...

6026SIsleRoyaleModeling
20 May 2018  Modeling Scenarios  Contributor(s):: Steven Morse, Brian Allen, Stanley Florkowski
The primary aim of this project is to draw a connection between differential equations and vector calculus, using population ecology modeling as a vehicle. This setting allows us to also employ multivariable optimization as a means of model fitting and multivariable integration in the context of...

6070SBeerBubbles
24 Apr 2018  Modeling Scenarios  Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

1105SAnimalFall
15 Apr 2018  Modeling Scenarios  Contributor(s):: Brian Winkel
This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.

3095SShotInWater
05 Apr 2018  Modeling Scenarios  Contributor(s):: Kurt Bryan
This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene: Do bullets moving through water slow as dramatically as depicted in the movies, so that someone a few...

1079SHomeHeating
30 Jan 2018  Modeling Scenarios  Contributor(s):: Kurt Bryan
This project concerns 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 or reheat it upon return? Both scenarios are analyzed in a series of exercises.

1066SUSCensusModeling
15 Sep 2017  Modeling Scenarios  Contributor(s):: Jean Marie Linhart
The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled.

1094SSteepingTea
12 Sep 2017  Modeling Scenarios  Contributor(s):: Eric Sullivan, Jesica Bauer, Erica Wiens
In this activity, we provide photographs of the steeping process for a fruit tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration of the tea oils in...

1091SSlopefields
04 Sep 2017  Modeling Scenarios  Contributor(s):: Ben Dill, Holly Zullo
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 the behavior of the solution curves. In this activity, students are introduced to the concepts of...

1115SModelingWithFirstOrderODEs
04 Sep 2017  Modeling Scenarios  Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model