Quantitative Skills > Teaching Methods > Teaching Quantitative Literacy > Exponential Growth and Decay

Exponential Growth and Decay

Geologic context: radioactive decay, population growth, changes in atmospheric CO2

Teaching Exponential Growth and Decay

by Jennifer M. Wenner, Geology Department, University of Wisconsin-Oshkosh
Jump down to: Teaching strategies | Materials & Exercises | Student Resources

Exponential growth and decay are rates; that is, they represent the change in some quantity through time. Exponential growth is any increase in a quantity (N) – exponential decay is any decrease in N – through time according to the equations:

N(t) = N0ekt (exponential growth)


N(t) = N0e-kt (exponential decay)


Teaching Strategies: Ideas from Math Education

Put quantitative concepts in context

There are a number of geologic contexts in which to introduce the concept of exponential growth and decay. Some of these include:

Use multiple representations

Because everyone has different ways of learning, mathematicians have defined a number of ways that quantitative concepts can be represented to individuals. Here are some ways that exponential growth and decay can be represented.

Use technology appropriately

Students have any number of technological tools that they can use to better understand quantitative concepts – from the calculators in their backpacks to the computers in their dorm rooms. Exponential growth and decay can make use of these tools to help the students understand this often difficult concept.

Work in groups to do multiple day, in-depth problems

Mathematicians also indicate that students learn quantitative concepts better when they work in groups and revisit a concept on more than one day. Therefore, when discussing quantitative concepts in entry-level geoscience courses, have students discuss or practice the concepts together. Also, make sure that you either include problems that may be extended over more than one class period or revisit the concept on numerous occasions.

Exponential growth and decay is a concept that comes up over and over in introductory geoscience: Radioactive decay, population growth, CO2 increase, etc. When each new topic is introduced, make sure to point out that they have seen this type of function before and should recognize it.

Teaching Materials and Exercises

Student resources

Geomaths has a page explaining the math behind radioactive decay with a link to a very nice MathHelp tutorial on exponential functions.

Mathworld has some very good resources explaining:

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