The logistic equation for the population (in thousands) of a certain species is given by $\frac{dp}{dt} = 9p - 4p^2$. Complete parts (a) through (d) below.
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The logistic equation describes the growth of a population $P$, where $t$ is measured in years. In each case, find (a) the carrying capacity of the population, (b) the size of the population when it is growing the fastest, and (c) the rate at which the population is growing when it is growing the fastest. $\frac{d P}{d t}=0.0002 P(1200-P)$
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The logistic equation describes the growth of a population $P$, where $t$ is measured in years. In each case, find (a) the carrying capacity of the population, (b) the size of the population when it is growing the fastest, and (c) the rate at which the population is growing when it is growing the fastest. $\frac{d P}{d t}=0.0008 P(700-P)$
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