A population is modeled by a function P that satisfies the logistic differential equation (see attached picture).?

a) If P(0) = 3, what is lim (x-->inf) P(t)?
If P(0) = 20, what is lim (x-->inf) P(t)?

b) If P(0) = 3, for what value of P is the population growing the fastest?

?2021-03-10T21:12:39Z

Hint: Graph p/5 * (1-p/12). 
Now, just interpret that curve, recalling that the vertical axis is p'.

You must have seen how to interpret it, no? 
At worst, solve the DE. 

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