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The population of rabbits on an island is modelled by the function \(P(t) = \frac{1000}{1 + 19e^{-0.4t}}\), where \(t\) is the time in months.
  1. Find the initial population of rabbits.
  2. State the carrying capacity of the island.
  3. Calculate the time required for the population to reach 800 rabbits.

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