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Unformatted text preview: Another way to say this is dP dt ∝ P = ⇒ dP dt = r P for some universal constant r that does not depend on the size of the population or the time t . (This constant is positive because our population grows as a function of time.) We will see later that this implies P ( t ) = P e rt where P is the initial size of the population. Unfortunately, this is not really the correct way to model population growth. Indeed, we do not expect population to grow without bound inde²nitely because we must take into account that there are limited resources, so there must be a limiting sustainable size K of the population. If the size P is greater than K we expect there to be a decrease in population because the population has exceeded its resources. Hence, we may assume that...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.
- Spring '09