11. Suppose ( P(t) ) denotes the size of an animal population at time ( t ) and its growth is described by the d.e. ( frac{d P}{d t}=0.002 P(1000-P) ). The population is growing fastest (A) initially (B) when ( P=500 ) (C) when ( P=1000 ) (D) when ( frac{d P}{d t}=0 ) (E) when ( frac{d^{2} P}{d t^{2}}>0 )
Added by Paisley P.
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002 P(1000-P) = 0 \] This equation is satisfied when either \( P = 0 \) or \( P = 1000 \). So, the critical points are \( P = 0 \) and \( P = 1000 \). Show more…
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