19. 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 is the number of individuals in the population, is the initial population size, is the maximum population size possible due to the various limiting factors, and r is a rate constant. Make a surface plot of versus t and assuming s–1, and . Let t vary between 0 and 100 and between 100 and 1,000.