I have two documents. Please read the PDF first and then answer questions
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: 0.9956 means that….; 0.0613 means 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,
[email protected] Follow this and additional works at: https://via.library.depaul.edu/depaul-disc Part of the Analysis Commons, Life Sciences Commons, Medicine and Health Sciences Commons, Numerical Analysis and Computation Commons, and the Social and Behavioral Sciences Commons 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://via.library.depaul.edu/depaul-disc/vol7/iss1/11 This Article is brought to you for free and open access by the College of Science and Health at Via Sapientiae. It has been accepted for inclusion in DePaul Discoveries by an authorized editor of Via Sapientiae. For more information, please contact
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[email protected] 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 birth 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 current population. When we look at survival rates, people have begun 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 rates 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 current 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:
[email protected] 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 required replacement rate of 2.0. However, we have yet to see a decrease in population which raises 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 current 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 by 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 0.9956273, 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 99.56273% 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 9 2 9 1 9 3 2 1 9 3 5 1 9 3 8 1 9 4 1 1 9 4 4 1 9 4 7 1 9 5 0 1 9 5 3 1 9 5 6 1 9 5 9 1 9 6 2 1 9 6 5 1 9 6 8 1 9 7 1 1 9 7 4 1 9 7 7 1 9 8 0 1 9 8 3 1 9 8 6 1 9 8 9 1 9 9 2 1 9 9 5 1 9 9 8 2 0 0 1 2 0 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 https://via.library.depaul.edu/depaul-disc/vol7/iss1/11 that will be born based on the current 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 current 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 based 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 correlation 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 current 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