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

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

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

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 Time (Min) Bacteri a Cells

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

Modern Notation Factorfrom both terms Verhulst’s Logistic growth model: Substitute or

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

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

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

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

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

United States

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

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

South Korea

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

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

Japan

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

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

India

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

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

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

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

Works Cited p%2Fpub%2Fipc%2Fwww%2Fidbsum.html