Thread: rates of change- population growth

The population of fish is modeled by the differential equation

dP/dt = 2p -0.01P^2

Where P is the nuber of fish after t years...

a) What is the maximum number of fish the tank can support ?

Ans : dP/dt= 0 hence P=0 or P=200 .... therefore @ P=200 its a maximum point...

b) Find P for which the population is increasing most rapidly... ?

Ans: I have no clue.. is it when d^2t/dP^2 =0 where there is a horizontal point of inflexion.. i.e when p=100 ??

can some one correct me on part b) ... Thanks

Also if anyone can...

find an explicity formula for P in terms of t....

I'm struggling with this one

I know we can do dt/dP = 1/p(2-0.01p)

then apply partial fractions.. and then integerate and then .... thats when its gets abit tricky...