Calc06_5day2 - 6.5 day 2 Logistic Growth Greg Kelly,...

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Unformatted text preview: 6.5 day 2 Logistic Growth Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2004 Columbian Ground Squirrel Glacier National Park, Montana We have used the exponential growth equation to represent population growth. kt y y e = The exponential growth equation occurs when the rate of growth is proportional to the amount present. If we use P to represent the population, the differential equation becomes: dP kP dt = The constant k is called the relative growth rate . / dP dt k P = → The population growth model becomes: kt P Pe = However, real-life populations do not increase forever. There is some limiting factor such as food, living space or waste disposal. There is a maximum population, or carrying capacity , M . A more realistic model is the logistic growth model where growth rate is proportional to both the amount present ( P ) and the carrying capacity that remains: ( M-P ) → The equation then becomes: Logistics Differential Equation ( 29 dP kP M P dt =- We can solve this differential equation to find the logistics growth model....
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This note was uploaded on 02/12/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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Calc06_5day2 - 6.5 day 2 Logistic Growth Greg Kelly,...

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