U.S. Population Growth: What Does the Future Hold?

To enable students to:

• gain some knowledge of the size of our U.S. population and its projected growth
• develop a deeper understanding of exponential growth
• recognize the differences and similarities between linear growth and exponential growth
• recognize the effect and implications of long-term exponential growth even when the growth rate is relatively small

This activity can be used in a College Algebra or Liberal Arts math class as an introduction to the nature of exponential growth and can be carried out in either a small class or a large lecture setting. A scientific or graphing calculator is required along with Internet access to display specific graphs of population data.

The time required for the entire activity is approximately 25-30 minutes but fewer segments can be offered as a shorter alternative (see Activity Description below for individual segment times).

Activity description

• Students are given a ConcepTest (Rich Text File 26kB Jul9 07) in the form of a straw poll (either show-of-hands or written) concerning the current U.S. population, its current growth rate, and a projection concerning the population in 2050. Each student is asked to make a conjecture and the instructor records the results for the class to see. (~5 minutes)
• The Question of the Day (Rich Text File 17kB Jul9 07) addresses the difference between a ten-year growth rate and an annual growth rate and also addresses the similarities and differences between linear and exponential growth. It begins with three ConcepTest questions and then students work in pairs to share and explain their answers and reasonings in written form. The instructor will need Internet access and a projector to display the specified population graphs for student viewing. (~10 minutes)
• CensusScope
  An easy-to-use tool for investigating U.S. demographic trends created and developed by the Social Science Data Analysis Network (SSDAN) at the University of Michigan.
• http://www.censusscope.org/us/chart_popl.html
• MERLOT description of CensusScope
• http://www.merlot.org/merlot/viewMaterial.htm?id=84539
• U.S. Census Charts and Tables
  U.S. Census Bureau data made more accessible and readable.
• http://www.census-charts.com/Population/pop-us-1790-2000.html
• MERLOT description of this Census Bureau data
• http://www.merlot.org/merlot/viewMaterial.htm?id=261555


• Lastly, students are asked to construct an exponential growth model and calculate future population values with the help of a graphing calculator in a write-pair-share activity (Rich Text File 86kB Jul9 07). They are also asked to describe and record the implications of these projected values. (~5-10 minutes)
• In conclusion, the instructor presents a summary of student results (~5 minutes)

The ConcepTest reveals how unaware many students are of the size of our current U.S. population and its annual growth rate (they are generally unaware of the sizes and growth rates of their city and state populations as well). In turn, the Question of the Day reveals that many students do not recognize the nature of exponential growth until it is clearly pointed out to them.

Lastly, the write-pair-share activity is designed to bring them to a realization of the dramatic results of our population growth if it were to continue at its present growth rate. Most students have never considered the mathematics involved and are somewhat shocked at the results.

I generally use this assignment as a means to provoke student thinking and reflection; grading is optional.

U.S. Census Bureau
Provides on-line access to census data, publications, and products
MERLOT description of the U.S. Census Bureau site
Direct link to the U.S. Census Bureau site