Populations starting out in closed environments grow slowly at first, when there

Question

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. 35 30 25 5 20 15 10 Answer parts a and b below 10 40 50 20 Time (days) 30 a. Use graphical techniques to graph the derivative of the fruit fly population, using the given graph of the population. Choose the correct graph of the derivative O A. B. 10 20 30 4050 Time (days) 10 20 30 40 50 Time (days) 1020 3040 50 Time (days) 10 20 30 4050 Time (days) b. During what days does the population seem to be increasing fastest? Slowest? Fill in the blanks The population seems to increase fastest during days and slowest during days

Explanation / Answer

As we can see derivative of given function in graph is zero at x=0. Then the slope of graph is increasing upto 28 or 30 days then it decreases to zero after that. Hence (a) and (d) are incorrect.

Now the maximum slope is in between 23 to 26 days and increment in number of flies during this time period is of approximately 50 flies. Hence slope is definitely more than 10. Hence (b) is also wrong. Now, the only option left is (c) which has to be correct.

Population growth is fastest during 22 to 27 days and slowest during start(t=0) and end(t=50)

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