Biologists stocked a lake with 500 fish and estimated the carrying capacity (the

Question

Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 3500. The number of fish tripled in the first year.

(a) Assuming that the size of the fish population satisfies the logistic equation dP/dt = kP (1 - P/K ) determine the constant k, and then solve the equation to find an expression for the size of the population after t years.
k= ?
P(t)= ?

(b) How long will it take for the population to increase to 1750 (half of the carrying capacity) ? answer in years

Explanation / Answer

a) That means the population will triple each year The equation would look like Y = 400 * 3^t where y = the population and t = the time in years so after one year the population would equal Y = 400 * 3^1 Y = 1200 which is triple b) The population equal 5000 5000 = 400 * 3^t 5000 / 400 = 3^t 12.5 = 3^t log 12.5 = t * log 3 t = log 12.5 / log 3 t = 2.299 years

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