Population Growth Of Various Countries

1. Population Growth Of Various Countries Jose Henson Sam Choi Natalie Wagner Alex Kang

2. Origins of Population Growth Models • Thomas Malthus proposed that human growth would precede exponentially • An essay on the principle of population as it affects the future improvement of society (1798) • Gave formula: • Growth Rate: • Predicted the world would soon outgrow its resources, with the ultimate destruction of mankind

3. Exponential Growth Exponential Population Growth: -Used for rapidly growing population - Bacteria, insects, rabbits -Assumptions -All individuals reproduce constantly and equally -Not valid for human population growth - Valid over a short period of time

4. Growth of Bacteria • Reproductive rate, r, is found from data by finding ratio of 2 • Exponential growth equation can now be used to calculate future populations • At t=100

5. Revision of the Population Model • Pierre-Francois Verhulst of Belgium - Suggested that there was a limit to population growth in 1838 - Growth Formula: - mu represents mortality caused by high population -as population increases growth is overshadowed

6. Modern Notation Verhulst’s Logistic growthmodel: Factor from both terms Substitute or

7. Population Model Population equation can be found by solving the differential equation Algebraic manipulation: Integrate with respect to t: Simplify:

8. Derivation Continued Exponentiate: Let : Simplify: Solve for P:

9. Logistic Population Growth Logistic Population Growth : M = Population Capacity A = Initial Population Constant r = Reproductive rate constant Assumptions: - Found via logistic regression line - Only valid over long periods of time

10. Calculating Regression Equations Linear Regression: - Commonly called “best fit” line Logistic Regression - Creates a “best fit” S-shaped curve

11. Population of the World Current Population: 6,442,658,699 people Growth Rate: 76,570,430 people per year Estimates: 2020: 7.6 Billion people 2030: 8.2 Billion people 2050: 9.1 Billion People

12. United States

13. Analysis of Population Levels Calculated Current Population at t=35 (In Millions) Actual Current Population = 295.734 Million People

14. Analysis of Population Growth Current Population Growth at t=35 Growth Rate:

15. South Korea

16. Analysis of Population Levels Calculated Current Population at t=35 (In Millions) Actual Current Population = 48.422 Million People

17. Analysis of Population Growth Current Population Growth at t=35 Growth Rate:

18. Japan

19. Analysis of Population Levels Calculated Current Population at t=35 (In Millions) Actual Current Population = 127.417 Million People

20. Analysis of Population Growth Current Population Growth at t=35 Growth Rate:

21. India

22. Analysis of Population Levels Calculated Current Population at t=35 (In Millions) Actual Current Population = 1080.264 Million People

23. Analysis of Population Growth Current Population Growth at t=35 Growth Rate:

25. Carrying Capacity Set P=M - .00001 Solve for t Year country will reach the carrying capacity: U.S.A: 2543 Korea: 2305 Japan: 2150 India: 2543

26. Conclusions There are TOO many people in the world…..Thomas Malthus was right….

27. Works Cited http://www.library.uu.nl/wesp/populstat/Asia/skoreac.htm http://geography.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=geography&zu=http%3A%2F%2Fwww.census.gov%2Fftp%2Fpub%2Fipc%2Fwww%2Fidbsum.html http://www.library.uu.nl/wesp/populstat/Asia/japanc.htm http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/mordifeqs/logistic.html http://en.wikipedia.org/wiki/Global_Population#Forecast_of_world_population http://www.mnforsustain.org/united_states_population_growth_graph.htm http://www.library.uu.nl/wesp/populstat/Asia/indiac.htm http://www.cia.gov/cia/publications/factbook/geos/in.html#People http://www.cia.gov/cia/publications/factbook/geos/us.html http://www.cia.gov/cia/publications/factbook/geos/ja.html http://www.cia.gov/cia/publications/factbook/geos/ks.html