A population y(t) of fishes in a lake behaves according to the logistic law with a rate of growth per minute a = 0. 003 and a limiting growth rate per minute b = 0. 1. Moreover, 0. 002 are leaving the lake every minute.



1. 1


Write the dierential equation which is satisfied by y(t). Solve it when the initial population is of one million fishes.



1. 2


Compute [tex]\lim_{t \to \infty} y(t)[/tex]



1. 3


How much time will it take to for the population to be of only 1000 fishes? What do you think about this model?