Question: (a) Show that if P satisfies the logistic equation (4), then (b) Deduce that a population grows fastest when it reaches half its carrying capacity.

(a) Show that if P satisfies the logistic equation (4), then

2P d?P k*P = k²P[ 1 dt?

(b) Deduce that a population grows fastest when it reaches half its carrying capacity.

2P d?P k*P = kP[ 1 dt?

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