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Downloads
Views
Date
Relevance
Modeling Scenario
260
views
159
downloads
0
comments
1-051-OneTankSaltModel-ModelingScenario
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...
compartment
salt
tank
mixing
flow
Modeling Scenario
206
views
186
downloads
0
comments
1-054-GrowthInFarmland-ModelingScenario
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...
fitting
farm
farmland
Modeling Scenario
247
views
161
downloads
0
comments
1-058-WaterClocks-ModelingScenario
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.
flow
Torricelli's Law
spigots
water clock
Modeling Scenario
207
views
255
downloads
0
comments
1-062-BacteriaGrowth-ModelingScenario
We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential equation, and parameter estimation using EXCEL spreadsheet.
bacteria
exponential
growth
Modeling Scenario
171
views
161
downloads
0
comments
1-063-ThreeHoleColumnOfWater-ModelingScenario
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.
falling
column of water
Torricelli's Law
multiple spigots
spigots
Modeling Scenario
205
views
108
downloads
0
comments
1-064-TorricelliBox-ModelingScenario
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.
groundwater flow
column of water
Torricelli's Law
water displacement
submerged box
Modeling Scenario
244
views
305
downloads
0
comments
1-065-AlgalBlooms-ModelingScenario
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.
direction fields
tool:dfield
algae
harmful algae blooms
population
compartment
Lake Chapala
Modeling Scenario
200
views
144
downloads
0
comments
1-066-USCensusModeling-ModelingScenario
The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.
data
logistic
population
Gompertz
census
goodness of fit
Modeling Scenario
156
views
81
downloads
0
comments
1-067-ModelingWithSigmoidCurves-ModelingScenario
The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.
logistic
Gompertz
sigmoid
Verhulst-Pearl
Modeling Scenario
171
views
118
downloads
0
comments
1-068-WaterBottleCooling-ModelingScenario
Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
b
Newton's Law of Cooling
water bottle
autonomous
bottle
Modeling Scenario
201
views
154
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model 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?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Modeling Scenario
176
views
96
downloads
0
comments
1-080-DrugAdministration-ModelingScenario
A simple drug administration situation is modeled with only two observations.
decay
bloodstream
drug
rate constant
administer
Modeling Scenario
207
views
140
downloads
0
comments
1-083-FallingMeteorites-ModelingScenario
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus...
falling object
drag
variable mass
factor ranking
meteor
meteorite
Modeling Scenario
225
views
221
downloads
0
comments
1-088-RoomTemperature-ModelingScenario
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
environment
climate
temperature
Newton's Law of Cooling
cooling
periodic function
Modeling Scenario
195
views
115
downloads
0
comments
1-089-SpreadOfDisease-ModelingScenario
In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...
SIR model
Proportion
derivative
difference quotient
Sleeping Beauty
contagious disease
Modeling Scenario
213
views
210
downloads
0
comments
1-090-EmptySphericalTank-ModelingScenario
We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
Volume
sphere
Torricelli's Law
timing
spherical tank
fluid
empty
Modeling Scenario
209
views
386
downloads
0
comments
1-091-InvestigatingSlopeFields-ModelingScenario
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.
slope fields
population
Modeling Scenario
183
views
155
downloads
0
comments
1-093-SucroseReaction-ModelingScenario
We offer data on the hydrolysis of sucrose in the presence of catalyst sucrase. We present students with several models and ask which model is best. We ask students to estimate parameters for the best model.
kinetics
Michaelis-Menten
hydrolysis
reaction
sucrose
Modeling Scenario
221
views
87
downloads
0
comments
1-104-InfectionRisk-ModelingScenario
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.
infection
logistic
exponential
covid
carrying capacity
Modeling Scenario
203
views
245
downloads
0
comments
1-114-EarthClimate-ModelingScenario
In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
climate
energy
temperature
linearization
phase lines
energy balance model
root finding
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