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## Resources

##### Includes clear efforts on Issues
Modeling Scenario
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##### 1-057-FiguringFluidFlow-ModelingScenario
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.
discharge tank Torricelli's Law Conservation of Energy fluid flow height liquid
Modeling Scenario
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##### 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
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##### 1-059-ContainerShapeFallingWater-ModelingScenario
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.
containers Torricelli's Law shape discharge coefficient
Modeling Scenario
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##### 1-060-SalesMarketing-ModelingScenario
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.
marketing Bass model sales consumer products innovators imitators
Modeling Scenario
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##### 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
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##### 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
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##### 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
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##### 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
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##### 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
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##### 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
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##### 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
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##### 1-071-NewtonWatson-ModelingScenario
Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis
temperature death Newton's Law of Cooling time of death Sherlock Holmes
Modeling Scenario
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##### 1-073-WaterExitBottle-ModelingScenario
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.
data water flow Torricelli's Law bottle
Modeling Scenario
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##### 1-074-BottleWaterFlow-ModelingScenario
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.
b water Torricelli's Law bottle
Modeling Scenario
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