Populations starting out in closed environments grow slowly at first, when there are relatively few members, then more rapidly as the number of reproducing individuals increases and resources are still abundant, then slowly again as the population reaches the carrying capacity of the environment.

a. Use the graphical technique of Example 3 to graph the derivative of the fruit fly population. The graph of the population is reproduced here.

b. During what days does the population seem to be increasing fastest? Slowest?

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Number of flies 350 300 250 200 150 100 50 0 10 20 30 Time (days) 40 50