Christopher Coughenour

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The Evergreen State College

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Sustainability and Changing Rates of Change part of Curriculum for the Bioregion:Activities
In this module, students explore variable rates of change and applications to sustainability. The first component of this module consists of two primers on rates of change for students and instructors to work through. The first primer discusses basic concepts related to quantifying rates of change. Another primer is provided that outlines the approach to mathematically modeling rates of change, particularly for non-renewable resources. Exponential growth and the logistic model of growth are presented, with two examples provided for students to work through. These primers could be given as individual learning assignments or could be integrated into a classroom discussion of rates of change (and even derivatives) with the questions from the primers given as homework assignments. These are appropriate for undergraduates of any level who have proficiency in algebra and modest experience with spreadsheet software. The second component of this module provides two exercises related to crude oil production rates in order to explore relevant sustainability issues. The only prerequisite needed to complete these exercises is an understanding of basic rates of change concepts, the logistic growth model, and spreadsheet proficiency at the level needed to complete the primers. Separate roblem sets are provided for students to analyze petroleum production rates first in the United States and then globally. These exercises guide students through the process of fitting a mathematical model to historical oil data and then critically analyzing the validity of such a model and its possible utility in predicting future oil production rates. All exercises are designed so that students who have not yet taken calculus may work through them and, thus, the 'discrete' case of the derivative (differences method) in analyzing rates of change and inflection points is utilized.