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Modeling Scenario

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 petrÃ³leo datos expansiÃ³n oil slick

Abstract

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.

Citation

Researchers should cite this work as follows:

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.

Authors

Author(s): Brian Winkel

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