Some populations initally grow exponentially but eventually level off. Equations of the
Chapter 4, Problem 81(choose chapter or problem)
Some populations initally grow exponentially but eventually level off. Equations of the form Pstd M 1 1 Ae2kt where M, A, and k are positive constants, are called logistic equations and are often used to model such populations. (We will investigate these in detail in Chapter 9.) Here M is called the carrying capacity and represents the maximum population size that can be supported, and A M 2 P0 P0 , where P0 is the initial population. (a) Compute lim tl ` Pstd. Explain why your answer is to be expected. (b) Compute lim Ml ` Pstd. (Note that A is defined in terms of M.) What kind of function is your result?
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