Teacher's Guide for Activity #6
Modeling Population Growth


Lesson # 7

Overview:

Students create linear, exponential, and quadratic models of U.S. population data to determine which function best represents U.S. population growth.

Objectives: 

  • Find linear, exponential and quadratic models of U.S. population data
  • Predict future populations based on each model
  • Compare predicted populations to given estimates
  • Determine which function best represents data
Notes to Teacher: 

Students will continue to use the spreadsheets or data files they assembled in Activity #3. They will add a linear graph, exponential graph, and quadratic graph (2nd degree polynomial) to their files. To do do this, they can first create a scatter plot then add a trend line for each of the types of models. They should note the Coefficient of Determination (r2) for each model.  They should also find the equation of each trend line. Using either the equation or the trend line extrapolated for 30 years on the graph, students should predict the population for 2000, 2010, and 2020. An example of how to do this is shown in the Population of the Southern Region of the U.S. Example Excel Spreadsheet File and also the Web Page Example.

Students can check to see which function is the best model for U.S. population growth in a number of ways:

  • Determine which has the highest Coefficient of Determination (r2)
  • Compare predictions for each model to those estimated by U.S. Census Bureau
  • Compare residuals for each model 

Optional exercises are provided for students to plot the residuals for each model and to look for two or more exponential models that might be combined to accurately represent the data. Instructions for how to do this are provide in Activity #6.