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Modeling Scenario

1-019-RocksInTheHead-Modeling Scenario

Author(s): Brian Winkel

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

Keywords: logistic growth parameter estimation experiment

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Abstract

Resource Image 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.

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Description

Sensitivity is a subject that invites notions of change, e.g., how sensitive is a system to a slight change in a variable? How discerning are we to change around us? If we could change the wattage to a light bulb some 5 feet from us from 100 to 102 watts, would we notice the change? How about from 100 watts to 500 watts?

We offer a description of a project which measures the ability of individuals to sense the discernible difference between the masses of small rocks. Basically, we lay out a number of small rocks. It is best if these rock samples are from the same ``geological stock," i.e. have the same density and color, and that they be smooth, for sharp edges have the effect of appearing heavier as the edge cuts into the bare hand holding the rock used to assess its relative mass, thus distorting one's perception (mass discernment) with another (pressure).

This experiment will require a number of volunteers to each conduct an experiment. The experiment consists of comparing the mass of a number of small rocks to a 100 g mass and simply saying, for each rock, if it has more mass or less mass than the 100 g mass and reporting observations on a score sheet, one sheet per individual. We shall summarize the data for our rock collection. Suppose we have n rocks and compute the percent of our population which says rock i, i = 1, 2, . . . , n has more mass than the 100 g mass. A discerning population should have a low percentage report that low mass rocks, say 20 g, have more mass than 100 g mass. Similarly, a high percentage might be expected to say a 180 g rock has more mass more than a 100 g mass.

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Authors

Author(s): Brian Winkel

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

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