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Biologists stocked a lake with `400` fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be `4700`. The number of fish grew to 630 in the first year.

a)Find an equation for the number of fish `P(t)` after `t` years
` P(t)=`   .

b) How long will it take for the population to increase to `2350` (half of the carrying capacity)?
It will take   years.