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The Verhulst model, given in the following equation, describes the growth of a population that is limited by various factors such as overcrowding and lack of resources:

where N(t) is the number of individuals in the population, N0 is the initial population size, Nˆž is the maximum population size possible due to the various limiting factors, and r is a rate constant. Make a surface plot of N(t) versus t and Nˆž assuming r = 0.1 s-1, and N0 = 10. Let t vary between 0 and 100 and Nˆž between 100 and 1,000.