Kanat 2011
Environmental Geology Homework Assignment – Exponential Growth Use the continuous compounding exponential growth relationship, Nt=N0eλt, to calculate world population given the following parameters: Initial year, t0: 2010 Final year, t60: 2070 Initial population, N0: 6,800,000,000 The rate of natural increase (RNI) is the rate at which a population is increasing (or decreasing) in a given year due to a surplus (or deficit) of births over deaths, expressed as a percentage of the base population. It differs from the growth rate which is defined as the number of persons added to (or subtracted from) a population in a year due to natural increase and net migration. The growth rate in the United States is 1.0% (USCB 2010). Region or Country Modeled (PRB 2011) λ, RNI (%) 0.6 United States 1.2 World Average 3.5 Niger 1. Calculate the population for every fifth year and plot the results on arithmetic and semi‐log graphs; scale the graphs so the years 2010 through 2070 fit nicely on one sheet. Label and annotate the graphs. 2. Complete Table 1 and include it in the narrative. RNI
population
λ (%)
2010
2050
2100
United States
0.6
World Average
1.2
Niger
3.5
Table 1. Population Worksheet (PRB 2011) Region
2200
3. The narrative should include the following: • A definition of exponential growth. • The conditions that must be met, and excluded, when using exponential growth to model a system. • A discussion of the validity of projections using both types of graphs. • A discussion of the visual impact of both types of graphs; incorporate the graphs within the text. • A discussion of Table 1; include Table 1 in the narrative. • Refer to the graphs as Figures 1 and 2; refer to the table as Table 1. • Print and submit the narrative; email the narrative and spreadsheet to les.kanat@jsc.edu. • The narrative should be single‐sided, 1.5 line spacing, 0.75” margins, and no less than 10‐point font. Limit the essay (excluding the title page, figures, and calculations) to no more than four pages. Title page should have an appropriate title, a date, your name, and be held together by one staple; paginate appropriately. Graphs should be uncluttered, neat, well labeled, and referred to in the text; be sure to use Excel to create the graphs. Grammar, parts of speech, noun‐verb agreement, and spelling are important, so write clearly and concisely. Use appropriate subheadings and include appropriate references. References Population Reference Bureau (PRB) 2011. DataFinder. Retrieved on 25 Jan 2011 from http://www.prb.org/DataFinder.aspx. U.S. Census Bureau (USCB) 2010. International Data Base. Retrieved on 27 Jan 2011 from http://www.census.gov/ipc/www/idb/worldpopinfo.php. Note: The USCB (2010) reported the total population of the world, projected to 27 Jan 2011, to be 6,896,068,557 people; the resident population of the United States to be 311,960,478 people; and the 2009 population of Vermont to be 621,760 people.