MATH 1030-005, Group Project Worksheet Spring 2010Group Members:Instructions: This worksheet must be turned in with the summary paper by April 14.Complete each question, and if you are asked to make a computation, show all of your work.Write neatly and legibly. Points may be deducted if answers are incorrect, incomplete, or messy.I. Population Growth in UtahThe linear and exponential models are commonly used in population projections. The goal ofthis project is to obtain a better understanding these models.1. Describe and compare linear and exponential growths.2. Give 5 examples of each type of growth explaining why it would be linear/exponentialgrowth (LG or EG).• Example 1:1• Example 2:• Example 3:• Example 4:• Example 5:3. The data of population in Utah over the last 100 years is given below.Year Population of Utah Year Population of Utah1900 276,749 1960 890,6271910 373,351 1970 1,059,2731920 449,396 1980 1,461,0371930 507,847 1990 1,722,8501940 550,310 2000 2,233,1691950 688,862 2003 2,351,4672(a) Determine whether the population in Utah has grown linearly or exponen-tially over the last 100 years. Justify your answer by using a graph andappropriate calculations of the absolute and relative changes over time.Years Absolute Change Relative Change1900-19101910-19201920-19301930-19401940-19501950-19601960-19701970-19801980-19901990-20003(b) According to your graph, what is the projected population in Utah? (Makean estimate.)II. Developing a Population ModelThe U.S. Census’s annual estimates of the resident population for incorporated places over100,000, ranked by July 1, 2008 population: April, 2000 to July 1, 2008 are given athttp : //www.census.gov/popest/cities/SUB − EST 2008.html .Using the data, answer the following questions.1. Select a U.S. city: .2. The city you chose above will be your city of interest now. Research and recordthe populations for your city in 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980,1990, 2000.Year Population of Your City Year Population of Your City1910 19601920 19701930 19801940 19901950 20003. Find the absolute and relative change in population during this period (decadeto decade and overall).4Years Absolute Change Relative Change1900-19101910-19201920-19301930-19401940-19501950-19601960-19701970-19801980-19901990-20004. Can you see any big gap in your data? Can you explain any big changes (if thatis the case)?5. Plot your data on a graph and draw a line the visually fits the data well.56. Find the equation of the line you drew for the previous question.7. Use the linear model (that you developed) to predict the population for 2001,2004, and 2008?Population for 2001:Population for 2004:Population for 2008:8. Develop an exponential equation to model your population data, and sketch iton your graph.69. What does this model predict for the year 2001, 2004, and 2008?Population for 2001:Population for 2004:Population for 2008:10. How do these values compare to the values you found using a linear model?For 2001:For 2004:For 2008:11. Find the estimated population for 2001, 2004, and 2008 using the U.S. Census website and compare it to the value that your models predicted.For 2001:For 2004:For 2008:712. In your opinion, which graph/model better represents the population of yourcity?
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