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Math Help - population

  1. #1
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    population

    A population of animals in an ecological niche is growing in time so that it's rate of growth dp/dt is related to its current size by the differential equation dp/dt = 900/p^2. If time is measured in years and initially there are P(0) = 10 animals present, find the population function P(t) giving the size of the population after t years.

    Don't get this, but I integrated it, am I suppose to plug 900 somewhere in the equation P=Ce^kt??
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    I am thinking that when t=0, C=10. Am I suppose to cancel out P to find out k or something?
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  3. #3
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    Quote Originally Posted by elpermic View Post
    A population of animals in an ecological niche is growing in time so that it's rate of growth dp/dt is related to its current size by the differential equation dp/dt = 900/p^2. If time is measured in years and initially there are P(0) = 10 animals present, find the population function P(t) giving the size of the population after t years.

    Don't get this, but I integrated it, am I suppose to plug 900 somewhere in the equation P=Ce^kt??
    I don't understand your question. If you integrated dP/dt= 900/P^2 (and that's the only derivative to integrate), the 900 is already in there! But you don't get P= Ce^kt. From dP/dt= 900/P^2 you get P^2 dP= 900 dt and integrating, (1/3)P^3= 900t+ C. Determine C in THAT by setting t= 0, P= 10 to get 1000/3= C. If you wish to solve for P, P^3= 2700t+ C, P= ^3\sqrt{2700t+ C}.
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