Tags: medium

Modeling Scenarios (21-35 of 35)

  1. 1-050-S-BargingAhead

    10 Feb 2016 | | Contributor(s):: Timothy Pennings

    As captain of a barge, you need to determine how fast to transportyour barge up river against the current in order to minimize the expended energy.Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if...

  2. 1-034-S-FishMixing

    24 Dec 2015 | | Contributor(s):: Eric Sullivan, Elizabeth Anne Carlson

    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 and fishing plan in a lake. The mixture is of two species of fish, one being the current sole...

  3. 1-022-S-SpreadOfTechnology

    27 Nov 2015 | | Contributor(s):: Brian Winkel

    We examine  plots on the  spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

  4. 1-011A-S-Kinetics

    06 Jun 2015 | | Contributor(s):: Karen Bliss

     Adapted from 1-11-Kinetics, SIMIODE modeling scenario.  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 study zeroth, first, and...

  5. 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...

  6. 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.

  7. 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.

  8. 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.

  9. 1-019-S-RocksInTheHead

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

     We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

  10. 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...

  11. 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...

  12. 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.

  13. 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...

  14. 1-005A-S-OilSlick

    30 May 2015 | | Contributor(s):: Karen Bliss

  15. 1-005-S-OilSlick

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

    We describe a modeling activity for students in  which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...