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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.