Presently the U.S. growth rate is about 1% per year. In addition, there are appr

Question

Presently the U.S. growth rate is about 1% per year. In addition, there are approximately 700,000 immigrants into the United States each year and approximately 160,000 emigrants from the United States each year (see flow diagram in Figure 1.17). For simplicity, assume all of the immigration and emigration occurs at the end of the year. Draw a flow diagram to model the changing U.S. population. Develop a discrete dynamical system to model the population size. Given that the population in January 1999 was about 271 million, use this dynamical system to predict the U.S. population in January 2003. We must note that the numbers given in this problem are very volatile and do not remain fixed over time. Thus, other factors would need to be considered to get a better model for predicting U.S. population size.

Explanation / Answer

HEre we starts with calculating total population at the end of each year.

So total population in year 2000 = initial population in year 1999 + 1% of initial population in year 1999 + (700000 -160000)

=271 + 0.01(270) + 0.54 = 271 + 2.71+0.54 = 274.25

Now total population in year 2001 = initial population in year 2000 + 1% of initial population in year 2000 + 0.54

= 274.25+0.01(274.25)+0.54 = 274.25 + 2.7425+0.54=277.5325

Similarly total population in the beginnning of year 2002 = 277.5325 +0.01(277.5325)+0.54

= 277.5325+2.775325 +0.54 = 280.847825

And lastly total population in the beginnning of year 2003 = 280.847825 + 0.01(280.847825) + 0.54

=280.847825 +2.80847825+0.54

=284.2

So total population in January 2003 is about 284.2 million.

Answer

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