(a) Show that if satisfies the logistic equation 4, then d2P / dt2 = k2P(1 - P...

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(a) Show that if satisfies the logistic equation 4, then
d2P / dt2 = k2P(1 - P / M) (1 - 2P / M)
(b) Deduce that a population grows fastest when it reaches half its carrying capacity.
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