MATH 1030-005, Group Project Worksheet
Spring 2010
Group 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 Utah
The linear and exponential models are commonly used in population projections. The goal of
this 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/exponential
growth (LG or EG).
• Example 1:
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• 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
1900
276,749
1910
373,351
1920
449,396
1930
507,847
1940
550,310
1950
688,862
2
Year Population of Utah
1960
890,627
1970
1,059,273
1980
1,461,037
1990
1,722,850
2000
2,233,169
2003
2,351,467
(a) Determine whether the population in Utah has grown linearly or exponentially over the last 100 years. Justify your answer by using a graph and
appropriate calculations of the absolute and relative changes over time.
Years
Absolute Change Relative Change
1900-1910
1910-1920
1920-1930
1930-1940
1940-1950
1950-1960
1960-1970
1970-1980
1980-1990
1990-2000
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(b) According to your graph, what is the projected population in Utah? (Make
an estimate.)
II. Developing a Population Model
The U.S. Census’s annual estimates of the resident population for incorporated places over
100,000, ranked by July 1, 2008 population: April, 2000 to July 1, 2008 are given at
http : //www.census.gov/popest/cities/SU B − 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 record
the populations for your city in 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980,
1990, 2000.
Year Population of Your City
1910
1920
1930
1940
1950
Year Population of Your City
1960
1970
1980
1990
2000
3. Find the absolute and relative change in population during this period (decade
to decade and overall).
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Years
Absolute Change Relative Change
1900-1910
1910-1920
1920-1930
1930-1940
1940-1950
1950-1960
1960-1970
1970-1980
1980-1990
1990-2000
4. Can you see any big gap in your data? Can you explain any big changes (if that
is the case)?
5. Plot your data on a graph and draw a line the visually fits the data well.
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6. 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 it
on your graph.
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9. 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 web
site and compare it to the value that your models predicted.
For 2001:
For 2004:
For 2008:
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12. In your opinion, which graph/model better represents the population of your
city? Explain.
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