Deer population Refer to Exercise. It can be shown by means of calculus that the rate R (in deer per year) at which the deer population changes at time t is given by R =− 4t3 + 42t.
Deer population A herd of 100 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number N(t) of deer after t years is given by N(t)=−t4 + 21t2 + 100, where t > 0.
(a) Determine the values of t for which N(t)> 0, and sketch the graph of N.
(b) Does the population become extinct? If so, when?
(a) When does the population cease to grow?
(b) Determine the positive values of t for which R > 0.
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