Tags: order

Modeling Scenarios (61-80 of 84)

  1. 1-026-S-Evaporation

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We provide data (in EXCEL and Mathematica files) on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We  ask students to develop a mathematical model for the rate of evaporation for the alcohol mixture...

  2. 1-025-S-MixingItUp

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

  3. 1-023-S-RumorSpread

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    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. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.

  4. 1-020-S-IceMelt

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer up the claim of a store catalog  that   its ice ball mold allows users to  "... make ice balls that outlast cubes and won't water drinks down."  We ask students to build a mathematical model to defend or contradict this claim.

  5. 1-018-S-LogisticPopGrowth

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic  model in these situations. 

  6. 1-017-S-DiseaseSpread

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways)  in a differential equation model for the spread of the disease. Students ...

  7. 1-016-S-DogDrugs

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer a problem of determining the necessary drug administration in order to keep a dogsedated with specific information on half-life for an exponentially decaying presence of the drug in the body.

  8. 1-015-S-Torricelli

    03 Jun 2015 | | Contributor(s):: Brian Winkel

    We  model the height of a falling column of water in a  right circular cylinder (radius = 4.17 cm) emptying through a small hole on the side of the cylinder.  Indeed, in all the videos below where are referred to in this Modeling Scenario the cylinder is a 2 liter soda pop...

  9. 1-013-S-Sleuthing

    03 Jun 2015 | | Contributor(s):: Brian Winkel

    We present several situations in which differential equation models serve to aid in sleuthing and general investigations. One involves initial speed given information about constant deceleration and distance to stop in traffic incident; one involves modeling a steel ball launched vertically and...

  10. 1-012-S-SublimationCarbonDioxide

    03 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer data on the sublimation of dry ice (carbon dioxide) with data collected in a classroom setting so that students can model the rate of change in the mass of a small solid carbon dioxide block with a differential equation model, solve the differential equation, estimate the parameters in...

  11. 1-011-S-Kinetics

    03 Jun 2015 | | Contributor(s):: Brian Winkel

    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We offer many opportunities to model these chemical reactions with data, some of which comes from...

  12. 1-045-S-TimeOfDeath

    02 Jun 2015 | | Contributor(s):: Brian Winkel

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

  13. 1-040-S-OutcomeSavings

    02 Jun 2015 | | Contributor(s):: Brian Winkel

    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.

  14. 1-031-S-CoolIt

    02 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer data on the temperature of water in a beaker which resides in a room of constant temperature and also in an environment of nonconstant temperature. Students are encouraged to consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets...

  15. 1-009-S-ICUSpread

    02 Jun 2015 | | Contributor(s):: Brian Winkel

    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

  16. 1-060-S-SalesMarketing

    01 Jun 2015 | | Contributor(s):: Brian Winkel

    We lead students through the development of a sales forecasting model based on marketing principles first espoused by F. M. Bass in 1969. We offer definitions, assumptions, model equations, differential equations, and data on sales over 15 year periods against which   models may be tested.

  17. 1-030-S-IntraocularGasBubbles

    01 Jun 2015 | | Contributor(s):: Brian Winkel

    SPANISH LANGUAGE VERSION  We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.cls. Names will be x-y-S-Title-StudentVersion-Spanish and x-y--T-Title-TeacherVersion-Spanish

  18. 1-007-S-AntTunnelBuilding

    31 May 2015 | | Contributor(s):: Brian Winkel

    We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION  We have placed in Supporting Docs both...

  19. 1-006-S-FinancingSavingsAndLoans

    31 May 2015 | | Contributor(s):: Brian Winkel

    We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose.  In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...

  20. 1-005B-S-ChemDataCollection

    30 May 2015 | | Contributor(s):: Brian Winkel

    We present a situation in which a chemistry graduate student is assigned the  task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...