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The Exponential Function, and what it can tell us about the Consumption of Non - renewable Resources John A. Adam

Other species may increase so rapidly that culling them may be the only option to control their popu lations, especially if they are predatory. Plankton blooms can appear in a matter of days if the condi tions are right. In this context, the word “ bloom ” implies explosive growth. Generally speaking, many people are unfamiliar with explosive growth and the functions that mod els it. This article draws attention to a specific function that addresses explosive growth before addressing the implications of non - renewable re sources we consume. In other words, nonlinear functions are usually better descriptors of depend ent variable time - behavior in the examples given above. This article focuses on exponential func tions, which are an important part of the High School content (see AII.6 & 7 and MA.2 & 4 in The Virginia Standards of Learning). Although many see the topic as irrelevant in prac tice, nothing could be further from the truth. Non linear functions models are used by non - profits, for profits, and governments around the world to find ways to reduce reliance on fossil fuels, which are non - renewable resources, in favor of a combination of solar, wind, geothermal, nuclear, and other “ Green ” technologies, due to the fossil fuel nega-

Introduction

Not everything in life is linear. That is, “ output ” is not always proportional to “ input. ” What is meant by that statement? It is helpful to consider possible ways that quantities change over time in the world around us. In principle, they may remain constant, grow or decline, or be cyclic. If so, they may not be modeled using a linear function. These basic types of change can be combined, that is, oscilla tions may grow or decline in amplitude as ob served with animal, fish or insect populations. Sometimes species of nature decline and eventual ly die out, becoming extinct. We all live with diurnal periodicities – day and night – and annual ones as the seasons change. There is evidence to suggest that the effects of global warming can extend the duration of other types of “ seasons ” such as wildfire and wet sea sons in some parts of the world. On a financial level we hope that our bank or sav ings accounts grow because of compound interest; credit card debt can grow if we are not careful. House prices may grow or decline depending on the market and economy. New cars generally de preciate once they have been driven of the dealer ship lot.

Virginia Mathematics Teacher vol. 48, no. 1

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