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Question: 8 the logistic model for population growth for many organisms...

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8. The Logistic Model for Population Growth For many organisms the rate of reproduction depends on the amount of space and resources available to each organism, which depends on how many other organisms these resources must be shared with. A model for such effects is to make the rate of reproduction (number of offspring produced in one year minus the number of deaths in one year) depend on the number of organisms, N. One model for this effect is the logistic equation, where r and K are positive constants. a. Assume initially that K 100. Draw a graph of R(N) and find its domain and range. b. We want to understand the role played in the model by the parameters r and K. First set K 100, and plot the function R(N) forr 1,2,3. Describe in words how the function changes. [Hint: Measure the maximum reproduction rate.] c. Now set r 1, and plot the function for K 100, 200, 300. K is often called the carrying capacity of the environment in which the organism lives. Explain why this term is used by looking at your graph.

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