## Tags: medium

### Modeling Scenarios (1-20 of 35)

1. 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 ...

2. 30 May 2015 | | Contributor(s):: Karen Bliss

3. 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...

4. 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.

5. 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...

6. 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...

7. 17 Mar 2017 | | Contributor(s):: Brian Winkel

We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''

8. 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,...

9. 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.

10. 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.

11. 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.

12. 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.

13. 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...

14. 02 Mar 2016 | | Contributor(s):: Sania Qureshi

We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom  is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

15. 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...

16. 07 Apr 2016 | | Contributor(s):: Rachelle DeCoste, Rachel Bayless

This activity is a gentle introduction to modeling via differential equations. The students will model the rate at which the word jumbo has propagated through English language texts over time.

17. 22 Jun 2016 | | Contributor(s):: Troy Henderson

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 internal temperature of the meat.  This data can be used to model and predict the amount...

18. 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...

19. 03 Jun 2016 | | Contributor(s):: John Thomas Sieben

Things float or they don’t.  Well, it’s not quite that simple. In this exercise we lead students through applications of several laws of physics to develop and solve differential equations that will predict where in a water column a weight with an attached lift bag will become...

20. 11 Sep 2016 | | Contributor(s):: Dan Flath

We offer students the opportunity to develop several 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 in state (or population size) n at time t. We go further...