Modeling Population Growth: Exponential and Hyperbolic Modeling

ABSTRACT

A standard part of the calculus curriculum is learning exponential growth models. This paper, designed to serve as a teaching aid, extends the standard modeling by showing that simple exponential models, relying on two points to fit parameters do not do a good job in modeling population data of the distant past. Moreover, they provide a constant doubling time. Therefore, the student is introduced to hyperbolic modeling, and it is demonstrated that with only two population data points, an amazing amount of information can be obtained, such as reasonably accurate doubling times that are a function of *t*, as well as accurate estimates of such entertaining topics as the total number of people that have ever lived on earth.

Cite this paper

D. Hathout, "Modeling Population Growth: Exponential and Hyperbolic Modeling,"*Applied Mathematics*, Vol. 4 No. 2, 2013, pp. 299-304. doi: 10.4236/am.2013.42045.

D. Hathout, "Modeling Population Growth: Exponential and Hyperbolic Modeling,"

References

[1] R. B. Banks, “Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics,” Princeton University Press, Princeton, 1999, pp. 138-145.

[2] The United States Census Bureau, “Atlas of World Population History”. http://www.census.gov/population/international/data/worldpop/table_history.php

[3] Google Public Data. http://www.google.com/publicdata/explore?ds=d5bncppjof8f9_&met_y=sp_pop_totl&tdim=true&dl=en&hl=en&q=world+population+data

[4] Hyperbolic Growth. http://en.wikipedia.org/wiki/Hyperbolic_growth

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[1] R. B. Banks, “Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics,” Princeton University Press, Princeton, 1999, pp. 138-145.

[2] The United States Census Bureau, “Atlas of World Population History”. http://www.census.gov/population/international/data/worldpop/table_history.php

[3] Google Public Data. http://www.google.com/publicdata/explore?ds=d5bncppjof8f9_&met_y=sp_pop_totl&tdim=true&dl=en&hl=en&q=world+population+data

[4] Hyperbolic Growth. http://en.wikipedia.org/wiki/Hyperbolic_growth

[5] “How Many People Have Ever Lived on Earth?” Population Today: News, Numbers and Analysis, November- December 2002, Vol. 30, No. 8. http://www.prb.org/pdf/PT_novdec02.pdf

[6] “With Earth’s Population Now at 7 Billion, How Many People Have Ever Lived,” Nancy Szokan, Washington Post, October 31, 2011. http://www.washingtonpost.com/national/health-science/with-earths-population-now-at-7-billion-how-many-people-have-ever-lived/2011/10/27/gIQA6SLtZM_story.html

[7] A. H. Pollard, “Mathematical Models for the Growth of Human Populations,” Cambridge University Press, Cambridge, 1973.

[8] J. Y. Song, “Population System Control,” Mathematical and Computer Modeling, Vol. 11, Springer-Verlag Publishing, Berlin, 1988, pp. 11-16.