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...
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