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									MATH 123 Calculus I
Assignment 1
Due Date: Monday, February 12, 2006

Instructions: Each group of three students should submit one typed report from the
group. This report should be well-written, describing the problem, your group's solution,
and any pertinent intermediate steps required to obtain that solution. Include
mathematical equations and diagrams where relevant. Each of the three group members
should be responsible for writing the report for one of the three assignments during the
semester. The group member who writes this report should be different from the group
members who write the reports for the other projects. List all group members' names and
identify the primary writer on your report.

Eric Schlosser, in Fast Food Nation, states that "Annual beef consumption in the United
States peaked in 1976, … . Although the nation's population has grown since the 1970s,
it has not grown fast enough to compensate for the decline in beef consumption."1 The
U.S. Department of Agriculture publicizes data that we can use to analyze these trends.2

                                              Per Capita Beef          Per Capita
                                  Population Consumption               Broccoli
                             Year
                                   (millions) (pounds/person)          Consumption
                                                                       (pounds/person)
                             1940          132.0                43.4
                             1950          151.2                51.2
                             1960          180.0                64.7
                             1970          204.0                84.4                 1.5
                             1977          220.2                91.5                 2.4
                             1980          227.7                76.4                 2.9
                             1983          234.3                78.5                 3.5
                             1986          240.7                78.7                 4.7
                             1989          247.3                68.9                 6.0
                             1992          256.9                65.9                 5.8
                             1995          266.6                66.4                 6.9
                             1998          276.1                66.5                 7.1
                             2001          285.3                66.0                 7.4
                             2004          293.9                65.8                 8.5


   1. Use your calculator to graph the U.S. population data verses time in a semi-log
      plot. Include a rough sketch of your graph on your paper that you hand in or
      include a snapshot of your calculator screen.

   2. Is the U.S. population growing exponentially? Explain your answer.

   3. Use exponential regression to find an exponential model for the U.S. population
      from 1977 to 2004.

       (continued on back)
      4. Use your exponential model to find the annual percent growth rate of the U.S.
         population.

      5. Use your calculator to graph the annual U.S. beef consumption per capita verses
         time in a semi-log plot. Include a rough sketch of your graph on your paper that
         you hand in.

      6. Is the annual U.S. beef consumption per capita decaying exponentially after
         1977? Explain your answer.

      7. Use exponential regression to find an exponential model for the annual U.S. beef
         consumption per capita from 1977 to 2004.

      8. Use your exponential model to find the annual percent decay rate of the annual
         U.S. beef consumption per capita.

      9. Calculate the total annual U.S. beef consumption for each year listed in the table
         and graph the total consumption verses time.

      10. Does the trend in the total consumption graph relate to the population percent
          growth rate and the per capita beef consumption percent decay rate? If so, how?

      11. Use your results to critique Eric Schlosser's statement.

      12. Determine whether or not the annual U.S. per capita consumption of broccoli has
          grown exponentially. Explain your answer.

      13. Determine whether or not the annual total consumption of broccoli has grown
          exponentially. Explain your answer.

      14. Use exponential regression to find an exponential model for the annual broccoli
          consumption per capita from 1970 to 2004. Use this model to find the annual
          percent growth rate of the U.S. broccoli consumption per capita. Why do you
          think that the trend in beef consumption and broccoli consumption are so
          different?




1
    Schlosser, Eric, Fast Food Nation, Houghton Mifflin, 2002, p. 142.
2
    Consumer Price Index Home Page, Bureau of Labor Statistics, U.S. Department of
    Labor, http://stats.bls.gov/cpi/, last modified on January 16, 2007.

								
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