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Math Help - rates of change- population growth

  1. #1
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    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
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  2. #2
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    Apr 2009
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    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...
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