Population Growth, Ecological Footprints, and Overshoot

This page is authored by Rikki Wagstrom, Associate Professor of Mathematics at Metropolitan State University, Saint Paul, MN.
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In this activity, students develop and apply linear, exponential, and rational functions to explore past and projected U.S. population growth, carbon footprint trend, ecological overshoot, and effectiveness of hypothetical carbon dioxide reduction initiatives.

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Learning Goals

From a sustainability perspective, this activity explores some basic ideas that will engage students in civil discourse leading to more effective decisions:

  • Currently, the Ecological Footprint of the United States is larger than the Biocapacity of the country, and it is due entirely to the country's Carbon Footprint.
  • If the population of the United States grows and the per capita Ecological Footprint of the country remains constant, then the total Ecological Footprint will grow and the per capita Biocapacity will decrease.
  • If the population of the United States grows, modest initiatives to reduce the country's total carbon footprint may be insufficient to eliminate overshoot.
From a mathematical perspective, this activity utilizes the following concepts and skills:
  • Mathematical modeling: developing and applying mathematical models for population growth, per capita Biocapacity, and total Carbon Footprints
  • Graphical and numerical interpretation
  • Making an argument using mathematics: stating assumptions, applying appropriate mathematical models, and interpreting results

Context for Use

This activity is designed for an intermediate or college-level algebra course, or in a pre-calculus course. Students are expected to be familiar with linear and exponential functions. We use this activity as a follow-up to an earlier activity which introduces the idea of a footprint and the mathematics of footprint estimation.

Description and Teaching Materials

The student handout for this activity is found in the following pdf file.

Student Handout for Overshoot Exploration (Acrobat (PDF) 424kB Mar16 13)

This is a three-part activity. The first part deals with population growth, the second part deals with the relationships between population growth, Ecological Footprint, and Biocapacity, and the third part explores hypothetical initiatives to end overshoot. The three-part nature of the activity allows instructors flexibility in how they use it in their classroom:
  • Instructors may choose to have students complete all three parts either independently or in small groups. The activity was designed to enable independent-learning.
  • Instructors may choose to work part of the activity in-class and then assign the remainder of the activity as a homework assignment.

Teaching Notes and Tips

If students are completing the activity independently, it is advisable to assign and grade the project in stages to allow students to receive feedback and correction along the way. This gives students the best possible chance of reaching the end of the activity without being confused or misguided.

For instructors that intend to do the bulk of the activity together with their class, a nice stopping point is right before exercise (20). Instructors can then assign the final three exercises as homework.

This activity requires students to keep track of several quantities. At some point, students may start to mix up Ecological Footprints and Biocapacities, per capita amounts and total amounts, and Carbon Footprints and Ecological Footprints. Instructors might encourage students to write down a list of all variable names and what they represent.

The amount of time required for this activity will depend entirely on how the instructor uses the activity. Parts one and two can be completed in a one-hour class period. Part three will require an additional class period.


Exercises (20)-(22) in this activity address the primary learning goals of this activity and can be used to assess student learning.

References and Resources

This activity was written in collaboration with the Global Footprint Network.

Population data in this activity were obtained from the World Population Prospects, the 2010 Revision developed by the Population Division of the Department of Economic and Social Affairs, United Nations.