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Estimate when the rabbit population grew most rapidly how

Question: The rabbit population on a small Pacific island is approximated by

P = 2000/! + e^{5.3 - 0.4t}

with t measured in years since 1774, when Captain James Cook left 10 rabbits on the island.

(a) Graph P. Does the population level off?

(b) Estimate when the rabbit population grew most rapidly. How large was the population at that time?

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