Biologist stocked a lake with $100$ fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be $11000.$ The number of fish tripled in the first year.

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1. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after $t$ years.
Answer: $P(t) =$

2. How long does it take the population to increase to $1000$?
Answer:

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