References for more information on the topics covered in this module
1. Coxford, Arthur F. et al, Contemporary Mathematics in Context: A Unified
Approach Course 1 Part B. Glencoe McGraw-Hill, New York: 1998. Pages 419454, 461-481.
This is a unit on exponential growth and decay. It includes some population data
and experiments.
2. Brown, Richard G. Advanced Mathematics: Precalculus with Discrete
Mathematics and Data Analysis. Houghton Mifflin, Boston: 1992. Pages 180186.
This is a section in the book that covers exponentials.
3. Biggs, Alton et al, Biology: The Dynamics of Life (North Carolina Edition).
Glencoe McGraw-Hill, New York: 2000. Pages 95-106.
This is a section in the book that explores population growth.
4. http://www.ash.udel.edu/ash/tutor/exponents/webdoc1.htm
This website offers a tutorial for those having problems with exponential
functions.
5. http://www.geocities.com/CapeCanaveral/Launchpad/2426/page53.html
This website explains exponential functions and shows graphs. It also has sample
questions with answers for students to analyze.
Topics for further study
1. A great extension of the 2-3 day module, would be for students to search the
internet to find population data for several years. The data could be for an animal
species, humans, etc. They could enter this data into the calculator or use a
spreadsheet to calculate exponential regression. They could then analyze what this
means and report back to the class.
2. Another topic that goes along with this is the idea of overpopulation or some kind
of limiting factor such as lack of food. Students could explore how this affects
the population by presenting the information to the class or writing a report.
3. One great extension would be to explore the different kinds of population change.
For instance immigration could be modeled with an equation such as y = a(b)x +
c. This could also model some sort of constant change in the population. For
example, if there is a group of fish in a pond, then this could represent adding a
certain number of fish per year, or catching a certain number per year.
4. There are many other kinds of population change models to explore. Another
idea is for students to study change through interactions or a combination of those
listed above.