For the purpose of this algebraic model, we will define our variables based on hypothetical data derived from global energy trends (simplified for calculation):
We will analyze two distinct functions:
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Through the application of linear functions and systems of equations—core concepts in Allen R. Angel’s Introductory Algebra—we have constructed a simplified but insightful model of the energy transition. The algebra suggests that despite a significant head start, fossil fuels will eventually be overtaken by renewables due to the superior growth rate (slope) of the latter.
This exercise demonstrates that algebra is not merely the manipulation of symbols, but a language for describing the world. As students progress through their mathematical education, the linear models learned in introductory courses serve as the foundation for the more complex exponential and logarithmic models required in advanced calculus and statistics.