Part 1 - Global Population

The goal of this section is to explore global changes in the population of the United States. The U.S. Census Bureau maintains a FTP server from which you can access a file (popclockest.txt) containing national population estimates between 1900 and 1999. Import this data into MATLAB or EXCEL.

1. Plot the U.S. population as a function of time. What do you conclude?
2. Can the growth of the U.S. population be modeled by a simple evolution equation of the form N(t+1) = (1+R) N(t), where t is in years? Why or why not? If so, find R.
3. Post-census population estimates are obtained as described on the U.S. Census Bureau methodology page (see for instance the methodology file for the 2017 vintage) and in the article by F.W. Hollman et al, entitled Methodology and Assumptions for the Population Projections of the United States: 1999 to 2100. Explain the formulas given in the Cohort-Component Method section of this article.
4. Given the following estimates (downloaded in 2005 from a now decommissioned US Census Bureau page), find the population of the U.S. in 2004:
   1. Population in 2001: 285,102,075.
   2. Births, deaths, and net international immigration:
      • 2001-2002: 4,006,985; 2,429,999; 1,262,159.
      • 2002-2003: 4,055,469; 2,432,874; 1,225,161.
      • 2003-2004: 4,099,399; 2,453,984; 1,221,013.

Part 2 - Age Groups

The goal of this section is to explore the evolution of the population of the United States using different age groups. Population estimates by five-year age groups from 2010 to 2016 can be obtained from the U.S. Census Bureau web site.

1. Use this information to plot the age distribution in the U.S. for different years.
   1. Has there been major changes in the last 4 years of this data set?
   2. The data has 18 age groups. Use the age distribution that you just plotted to define larger age groups that can be used in a simplified model.
2. Using recent birth and death rates estimates, as published by the Center for Disease Control and Prevention, predict the population in the various age groups, taking the 2010 base estimates as initial condition. You may look at Figures 2 and 3 in these documents, respectively. (Note: do not attempt to print these files; they are more than 50 pages long!)
   1. How does your model compare to the estimates for 2016?
   2. Use your model to predict the population in each age group in 2050. What do you conclude?