1-043-CoolingUpAndDown-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/WQ82-BK11

We consider modeling the attempt of an air conditioner to cool a room to a ``constant'' temperature.

1-044-CollegeBound-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/8HCN-A297

Preparing for four years of college for a friend of the family's newborn is the task. Making assumptions about costs, timing, interest rates, and fiscal capabilities are the order of the day.

1-045-TimeOfDeath-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/4XES-BY10

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

1-005A-ChemDataCollection-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/7RF7-Z482

A student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting data. She only collects data at the start and end of a number of ten minute intervals and does not keep track of when the observations are made.

1-003-CollegeSavings-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/W59N-AZ87

We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.

1-047a-CondensationOptimization-ModelingScenario

25 May 2022 | Contributor(s): Chris McCarthy, Brian Winkel | doi:10.25334/2BMA-GJ13

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 walls and condenses on the bottom wall.

1-047-Condensation-ModelingScenario

25 May 2022 | Contributor(s): Chris McCarthy, Brian Winkel | doi:10.25334/FPKF-6M80

We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and data is offered for modeling with a differential equation.

1-001B-DeathImmigrationMystery-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/VVDS-GP62

We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student - of that student's choice

1-011-Kinetics-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/SY19-6444

We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.

1-051-OneTankSaltModel-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/CWHB-5N05

A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank and flows

1-052-SaltWaterTanks-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/GCQ6-7T80

We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.

1-055-WaterFallingInCone-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/DH95-PX63

We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.

1-057-FiguringFluidFlow-ModelingScenario

25 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/QXD4-FV90

We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

1-058-WaterClocks-ModelingScenario

24 May 2022 | Contributor(s): Sania Qureshi, Brian Winkel | doi:10.25334/FN59-0J23

We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out.

1-059-ContainerShapeFallingWater-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/G808-YA15

We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.

1-060-SalesMarketing-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/D4F3-M836

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

1-061-PotatoCooling-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/JPH7-B284

We model the cooling of a baked potato and compare it to student-collected data.

1-063-ThreeHoleColumnOfWater-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/2ZDT-7B90

We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

1-064-TorricelliBox-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/0H5H-6903

The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.

1-071-NewtonWatson-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/NDND-TE69

Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis

1-073-WaterExitBottle-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/1DP2-JN10

We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.

1-074-BottleWaterFlow-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/20H8-E231

We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.

1-080-DrugAdministration-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/DEHV-2F14

A simple drug administration situation is modeled with only two observations.

1-085-DrugBolus-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/8H4J-HG19

Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?

1-086-MedicinalPill-ModelingScenario

24 May 2022 | Contributor(s): Brian Winkel | doi:10.25334/EF8C-HF21

Administration of a medicinal pill in single and multiple doses is modeled.