Conservation Science—Fish Propagation: In order to generate income from public resources,...

Conservation Science—Fish Propagation: In order to generate income from public resources, the Crogan city council decides to stock Lake Simpson with commercial catfish. From past data collection, conservation scientists determine that the population of the stocked lake can be modeled by the function

where t represents the number of months since the lake was initially stocked and P(t) represents the population size.

(a) How many catfish were initially stocked in Lake Simpson?

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(b) Determine P′(t).

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(c) Evaluate and interpret P(12) and P′(12).