1060 Project 1 Population of Colorado fall 23
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School
University of Colorado, Denver *
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Course
1060
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
2
Uploaded by ProfessorGalaxyStarling41
Math 1060-007 Guided Project #1
Due Date: Wednesday October 11
th
Procedure:
1.)
You may work alone or with one partner on the guided project.
If you work with a partner, only one
paper will be turned in for the group and each person will receive the same grade
.
You may also work
individually as well, but then you are responsible for all the work yourself.
Groups or individuals may
not share any of their work with other groups or individuals.
2.)
Graphs must be created electronically with either Desmos or Excel.
Hand sketches of scatterplots and
graphs will receive no credit.
3.)
In addition to your graphs, follow the steps outlined in the guided project and
include the step
numbers in your paper
.
Read the questions carefully and be sure to answer each question in complete
sentences using correct grammar and spelling.
4.)
You may write up the answers to the project questions by hand or you may type them up.
If you type
the project, then math symbols can be typed and formatted using an equation editor such as MathType
or Microsoft Equation.
5.)
Tables, scatterplots, and graphs should be labeled and referenced appropriately.
Scatterplots and
graphs must be created using technology!
You should use Desmos or Excel and take screen shots.
Grading:
The guided project is worth 25 points.
The project will be evaluated on the following:
15 points
Written answers to questions will be graded on content, thoroughness and
thoughtfulness.
10 points
Graphical Representations and tables should be clear and easy to interpret.
1
Fall 2023
Population of Colorado
The population of Colorado grew steadily from the creation of Colorado Territory in February 1861. In this
project you will investigate whether this growth can be reasonably represented by one of the several simple
continuous functions. The data are decennial census data collected by the Census bureau. The data is collected
for the purposes of Congressional apportionment and is the basis of many governmental decisions. Our data
covers years from 1910 to 2020.
1.
The table on the right gives the population of Colorado
from 1910 to 2020.
Create a scatterplot for this data and
insert the scatterplot in your report.
Let
x
be the number
of years after 1910.
Do not use the years themselves for
x.
2.
Perform a “quadratic regression” using Desmos or Excel.
Record the resulting regression equation and insert a copy
of the graph of the function overlaid on top of a new
graph of the scatterplot.
This graph should be separate
from the graph you created in step 1 above. Round
coefficients and constants as given by Desmos.
3.
Now perform an “exponential regression” using Desmos
or Excel.
Record the resulting regression equation and
include a new graph of the function overlaid on the
scatterplot.
This graph should be separate from the
previous graphs that you have created.
Again, round
coefficients and constants as given by the software.
4.
Perform a “cubic regression” using Desmos or Excel.
Record the resulting regression equation and
include a new graph of the function overlaid on a new graph of the scatterplot.
Round coefficients and
constants as given by the software.
5.
Which model (quadratic, exponential or cubic) do you think fits the data points best? Explain.
6.
What will the predicted population of Colorado be in the 10 years after the last census (2021 – 2030)
according to each of the three models?
Organize your answers in a table.
7.
Use each model (exponential, quadratic and cubic) to predict when the population of Colorado will hit
the 10 million mark. Which model do you think may be best at making this prediction?
Explain.
8.
Reflection.
Write a summary (1 or 2 paragraphs is fine) reflecting on what you have learned in this
project.
2
Year
X = Number
of years
after 1910
Population of
Colorado
Data for L1
Data for L2
1910
0
799,024
1920
10
939,629
1930
20
1,035,791
1940
30
1,123,296
1950
40
1,325,089
1960
50
1,753,947
1970
60
2,207,259
1980
70
2,889,964
1990
80
3,294,394
2000
90
4,301,261
2010
100
5,029,196
2020
110
5,773,714
Source: Census Bureau
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