Question

05.02.   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 6900. 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 3450 (half of the carrying capacity)?
It will take........................ years.

Answer 1

Guen dota as 500 K 690O dt Plt Bk -Kt uhae Po faiol population. So 500 x 600 Plt) - (6400-500)e-Kt 500 3450000 -kt 6400500 Pu) x 500 PC) 1500 30 50000 1500 64.00e 500 2450000 1500 64ODe 500

640 ekご1800 32- k26 85 K2685 9450000 -12685t 6400 e 500 bT populaon Rceased to 3450 / 3450 34 50000 6400e Plt) 1.268t + 500 1.26854 GuSDe 3450000 +500 34SD 2685t 4ove SUD FLODD 12685t 6400e 500 t.268St 64 -268st In 5 6 .2685 It oiu take