Assignment
Deadline: 11/22/2021 4:00AM(Chicago time)
This assignment requires math modeling skill and must be professional in math (matrix).
You must read the article first (The PDF Docs) and then answer for questions below.
Questions based on the table 1. I don’t really understand the explanation from article so DON’t copy it. I want your own explanation and I can understand easily.
Question 1:
Please explain clearly for all the entries with BLUE highlighted.
(format: XXXXXXXXXXmeans that….; XXXXXXXXXXmeans that…)
Question 2:
Please explain clearly for the entries with YELLOW highlighted for 0 to 9 yrs, 10 to 19yrs and 80 to 89 yrs.
Question 3:
The entries like 0.9956, 0.9976, 0.9928, these data, where and when(which year) are they gained? Are these data reliable to represent the population in 2050?
Question 4:
How to calculate 1.3720? (Explain in your own understanding)
Question 5:
What is the difference from this population matrix model (table 1) and Leslie matrix ?
Question 6:
Could you see mortality rate from the table 1? How?
Question 7:
If I want to lower the immigration rate down to 1%, how the matrix model would look like? (Just show me the matrix)
United States Population Future Estimates and Long-Term Distribution
DePaul Discoveries DePaul Discoveries
Volume 7 Issue 1 Article 11
2018
United States Population Future Estimates and Long-Term United States Population Future Estimates and Long-Term
Distribution Distribution
Sean P. Brogan
DePaul University, sean
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Recommended Citation Recommended Citation
Brogan, Sean P. (2018) "United States Population Future Estimates and Long-Term Distribution," DePaul
Discoveries: Vol. 7 : Iss. 1 , Article 11.
Available at: https:
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ary.depaul.edu/depaul-disc/vol7/iss1/11
This Article is
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____________________________________
1
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Research Completed in Summer 2017
United States Population Future Estimates
and Long-Term Distribution
Sean Brogan1
College of Computer Science and Digital Media, Math and Computer Science
Ilie Ugarcovici, PhD; Faculty Advisor
Department of Mathematical Sciences
INTRODUCTION
Throughout the history of the United States, we
have never had a year that presented us with a
lower population than the year prior. This can be
attributed to women on average having more than
two live births during their lifetime [7]. Having
two children on average means that the rate of
irth is equal to the rate of death, with the two
children replacing their parents as far as
population is concerned. In a practical sense, this
means that with no change in mortality rates, we
could maintain the cu
ent population.
When we look at survival rates, people have
egun to live much longer. Particularly over the
last 35 years, there has been a continuous rise in
life expectancy (see Figure 1). This creates a
larger net population with fewer people exiting
the equation year after year.
Therefore, with increasing life expectancy and
enough children being born to increase the
overall population, we have experienced
significant growth as a nation.
We also see a noticeable impact on the population
from immigration and emigration. The United
States receives far more immigrants than the
number of emigrants which is yet another reason
for the consistent increase in the overall
population [6, 8, 9].
It is interesting to note that before 1960, fertility
ates were much higher than two children per
woman creating a large net growth in overall
population. Between 1960 and 1974, however,
there was a steady decline in the birth rate.
During the next 40 years, fertility rates, while
ABSTRACT The population of the United States has always increased year after year. Even now with
decreasing birth rates, the overall population continues to grow when looking at conventional models.
The present study specifically examines what would happen to the U.S. population if we were to
maintain the cu
ent birth and survival rates into the future. Our research shows that by 2050, the U.S.
population will become much older and cease to grow at all.
1
Brogan: US Population Future Estimates and Long-Term Distribution
Published by Via Sapientiae, 2018
mailto:
XXXXXXXXXX
much lower, did not change significantly (see
Figure 2). As of 2014, the birth rate was down to
1.86 births per woman, which is lower than the
equired replacement rate of 2.0. However, we
have yet to see a decrease in population which
aises the question: Should we be concerned by
the lower birth rate? The point of our research
was to discover what would happen in the long
term if the cu
ent birth, mortality, and
immigration rates remained consistent.
METHODS
We decided to use a matrix model to predict
future growth due to both its simplicity and its
versatility (see Table 1). A matrix can be thought
of as a mathematical spreadsheet. Statistical data
is provided for the given rows and columns. Then
y taking a set of known data, such as the US
population from a certain year, and applying it to
the matrix, future predictions can be made.
For example, position (2,1), with the value
XXXXXXXXXX, represents the number of people from
the 0 to 9 age grouping that will move on into the
10 to 19 age grouping after one iteration. This is
effectively stating that XXXXXXXXXX% of people live
through the first 10 years of their life. Similarly,
position (1,3) represents the number of children
Figure 1. United States Life Expectancy
Figure 2. United States Fertility Rate
0
10
20
30
40
50
60
70
80
90
1
9
0
2
1
9
0
5
1
9
0
8
1
9
1
1
1
9
1
4
1
9
1
7
1
9
2
0
1
9
2
3
1
9
2
6
1
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2
9
1
9
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0
0
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0
4
2
0
0
7
United States Life Expectancy
0
0.5
1
1.5
2
2.5
3
3.5
4
United States Fertility Rate
2
DePaul Discoveries, Vol. 7 [2018], Iss. 1, Art. 11
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that will be born based on the cu
ent size of the
20 to 29 age group. This means that 46.2% of the
20-29 age grouping will have a child that will be
added to the new 0 to 9 group after one iteration.
A matrix model works well here since we are
attempting to see what would happen if cu
ent
trends were to continue. If our birth rates or
mortality rates were to be calculated by some
means which would change them with each cycle,
this would no longer be the best approach.
Splitting the population into 10-year age groups
and accounting for immigration, we used a 9 x 9
matrix with age groups 0-9, 10-19, 20-29,…,70-
79, and an 80+ category which will be discussed
in more detail later. We pulled data from several
government sources ranging from the U.S.
Census Bureau to the CIA [1, 2, 6].
Birth rates were calculated by individual age
grouping using data from 2014 as we were trying
to see what would happen if those rates remained
consistent.
We took our mortality rates from 2007, as those
were the most up-to-date figures published in age
groupings of 10 years.
Finding accurate figures on immigration into the
U.S. is a difficult task, and the numbers vary
ased on the source being used. We looked at the
average number of legal immigrants coming to
the United States on a yearly basis. To keep the
figures consistent with our model, we then found
a co
elation between the number of immigrants
and our total population.
This was preferable since the only other option
would have been to simply add a base figure at
the end of each period. Adding a static number,
while accurate for the period from which it was
taken, would create inaccuracy in the long term
since historically, as the world’s population has
increased, immigration has also increased.
Therefore, by basing our immigration on the
cu
ent U.S. population for each period, we
maintain accuracy because the figure updates
dynamically with the rest of the population.
We found that over the last 20 years the U.S.
generally gained an immigrant population of
approximately 0.3% of its total population each
year. This means that if the U.S. had a total of
300 million citizens, it would gain 900 thousand
citizens through legal immigration by the end of
the year. Since we were working in 10 year gaps
for our model, we added 3% of the total
population to each interval.
In reviewing the data in Table 1, it may seem
contrary that one of the age groups is passing
along 137.2% to the next age group. The reason
this was done was to account for those individuals
who