Biologists stocked a lake with 800 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 7900 . The number of fish grew to 930 in the first year. a)Find an equation for the number of fish $$ P(t) $$ after $$ t $$ years. Use a growth rate $$ (k) $$ value of three decimal places. $$ P(t)=\frac{7900}{1+8.875 e^{-0.1694 t}} $$ b) How long will it take for the population to increase to 3950 (half of the carrying capacity)? It will take You may enter the exact value or round to two decimal places.

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a) The equation for the number of fish $$ P(t) $$ is: $$ P(t) = \frac{7900}{1 + 8.875 e^{-0.1694 t}} $$ b) It will take approximately 12.91 years for the population to reach 3950 fish.

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