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2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution

In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.

Probability Mean Poisson process birth and death process infinite number of differential equations

Modeling Scenario

870

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3258

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1-005-OilSlick-ModelingScenario

We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.

model fitting spreadsheets Spanish derrame de petróleo datos expansión oil slick

Modeling Scenario

284

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1-008-HangTime-ModelingScenario

We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''

gravity hang tim Newton's Second Law of Motion jump shot

Technique Narrative

118

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1-002-IntegratingFactor-TechniqueNarrative

We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.

Integrating Factor

Modeling Scenario

138

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1-097-SwimmingPool-ModelingScenario

This project involves the dynamics of chlorine concentration during regular swimming pool maintenance cycles. Students will have the opportunity to use both analytic and numerical methods.

concentration c chlorine numerical error swimming pool horine erreor

Modeling Scenario

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1-025-MixingItUp-ModelingScenario

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.

compartment salt tank mixing

Modeling Scenario

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1-021-FeralCatControl-ModelingScenario

Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of trap-neuter-return (TNR) as a control method for feral cat...

population growth control feral cats population control neuter trap-kill trap-neuter-return

Modeling Scenario

106

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1-039-StochasticPopModels-ModelingScenario

We develop 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.

Probability population dynamics Variance Mean stochastic deterministic

Modeling Scenario

114

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1-040-OutcomeSavings-ModelingScenario

We ask students to build a model for a savings account and to determine the monthly deposit in a savings account in order meet a long term savings goal.

Pop_Growth Pilot savings growth deposit g

Modeling Scenario

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1-041-AirToTop-ModelingScenario

One common rule taught to SCUBA divers is to ascend no faster than thirty feet per minute. In this project we will examine safe variable ascent rates, time required for a safe ascent using variable ascent rates.

SCUBA ascent air management breathing diving underwater

Modeling Scenario

148

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1-042-KoolAid-ModelingScenario

Students run experiments involving concentrated solution of drink powder flowing from upper to lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks, record data, and build...

concentration compartment tanks KoolAid

Modeling Scenario

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1-045-TimeOfDeath-ModelingScenario

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

body mass temperature death Newton's Law of Cooling body temperature

Modeling Scenario

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1-001B-DeathImmigrationMystery-ModelingScenario

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

m&m Mystery Novels immigration experiment death

Modeling Scenario

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1-052-SaltWaterTanks-ModelingScenario

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.

salt tank mixing

Modeling Scenario

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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