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Views
Date
Relevance
Modeling Scenario
386
views
398
downloads
0
comments
1-102-CancerTumor-ModelingScenario
This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
optimization
logistic
prediction
data fitting
power law
Gompertz
cancer growth
eponential
Bertalanaffy
Modeling Scenario
300
views
580
downloads
0
comments
1-170-CensusModeling-ModelingScenario
Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use.
logistic growth
exponential
population
U.S. Census Data
assumption
Google Sheets
Unites States
Guatemala
Modeling Scenario
293
views
574
downloads
0
comments
10-100-InsectOutbreaks-ModelingScenario
We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.
ecology
climate change
insect
insect outbreaks
insect outbreak
solitary wave
Modeling Scenario
286
views
228
downloads
0
comments
1-078-MonodGrowthModel-ModelingScenario
Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
bacteria
nutrient cycles
growth
Monod
consumption
Modeling Scenario
544
views
278
downloads
0
comments
1-104A-T-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 and comparing to actual disease data sets.
regression
infection
COVID19
carrying capacity
logistic equation
exponential model
Modeling Scenario
1200
views
1266
downloads
0
comments
1-070-FisheryHarvest-ModelingScenario
Students model with logistic growth, harvesting, and diffusion in analyzing ocean fisheries of the Atlantic cod. We help students build models, ever more complex, to capture physical realities. At each stage we ask students to reflect on the model.
logistic
Diffusion
management
harvest
fishery
Modeling Scenario
311
views
37
downloads
0
comments
1-018-LogisticPopModel-ModelingScenario
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...
data analysis
parameter estimation
logistic
Ciliate protozoa
population
limited growth
paramecia
Gause
Modeling Scenario
643
views
545
downloads
0
comments
1-032-WordPropagation-ModelingScenario
This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
Google
exponential growth
language
word problems
etymology
Ngram
propagation
Jumbo
Modeling Scenario
282
views
186
downloads
0
comments
5-023-FakingGause-ModelingScenario
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competition in the 1930's studies of G. F. Gause in the Soviet Union.
competition
logistic
yeast
Gause
paramecium
poplulation
Modeling Scenario
223
views
247
downloads
0
comments
6-029-TumorGrowth-ModelingScenario
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
Pop_Growth Pilot
logistic
comparment
tumor
synthetic data
sum of squares error
Modeling Scenario
363
views
260
downloads
0
comments
6-040-StruggleForExistence-ModelingScenario
We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters
competition
logistic
carrying capacity
paramecium
Modeling Scenario
330
views
224
downloads
0
comments
1-100-EngineeringDemographics-ModelingScenario
Students show how models can be used to examine social issues. The students examine three different models and use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women in the United...
logistic
population
Improved Euler Method
Gompertz
demographics
women
autonomous
Modeling Scenario
204
views
177
downloads
0
comments
1-109-EmployeeAttrition-ModelingScenario
This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations.
population
linear growth
decay
employee
attrition
Modeling Scenario
251
views
189
downloads
0
comments
1-053-SlimeSpread-ModelingScenario
We offer a video showing real time spread of a cylinder of slime and challenge students to build a mathematical model for this phenomenon.
spreadsheets
slime
Modeling Scenario
362
views
202
downloads
0
comments
6-021-AcornsRodentsSnakes-ModelingScenario
Students are given the opportunity to build a three tropic level model in which snakes eat rodents, rodents eat acorns, and acorns grow and occasionally mast.
predation
forest
snakes
rodents
acorns
trophic level
masting
Modeling Scenario
299
views
316
downloads
0
comments
1-019-RocksInTheHead-Modeling Scenario
We describe an experiment with data on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. Students use the logistic differential equation as a reasonable model and estimate parameters.
logistic growth
parameter estimation
experiment
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