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📚 Modeling, Functions, and Graphs
Chapters ▾
1 Functions and Their Graphs2 Modeling with Functions3 Power Functions4 Exponential Functions5 Logarithmic Functions6 Quadratic Functions7 Polynomial and Rational Functions8 Linear Systems9 Sequences and Series10 Algebra Skills Refresher11 Using a Graphing Calculator12 Using a GeoGebra Calculator App13 Glossary14 Properties of Numbers15 Geometry formulas16 GNU Free Documentation License

Chapter 2: Modeling with Functions

earth: Christian Michaels/Getty Images

World3 is a computer model developed by a team of researchers at MIT. The model tracks population growth, use of resources, land development, industrial investment, pollution, and many other variables that describe human impact on the planet.

The figure below is taken from Limits to Growth: The 30-Year Update. The graphs represent four possible answers to World3's core question: How may the global population and economy interact with and adapt to Earth's limited carrying capacity (the maximum it can sustain) over the coming decades?

models of world population limits

In this chapter, we examine the properties and features of some basic nonlinear functions and how they may be used as mathematical models.

Modeling, Functions, and Graphs by Katherine Yoshiwara (yoshiwarabooks.org), GNU Free Documentation License 1.2 or later. Adapted for the XYZ HTML edition with the authors' permission (recorded 2026-07-04). License: GFDL-1.2-or-later.