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Modeling Scenario

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1-005-OilSlick-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: model fitting spreadsheets derrame de petróleo datos expansión oil slick

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Abstract

Resource Image 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.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

This Modeling Scenario has an English and Spanish version.

An oil slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched to photograph the oil slick. On each trip, the helicopter arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. On each of seven trips the size (in area) of the slick is measured from both photographs.

Build a model for the size of the oil slick at time t.

Predict the future size of the oil slick, say at t = 10 min, t = 20 min, t = 120 min.

Plot your model of the size of the oil slick as a function of time.

Find the time at which the oil slick is 8 square miles.

Determine the time of each of the observations for the first, third, fifth, and seventh initial observations.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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