# population

• Feb 9th 2009, 08:32 AM
elpermic
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??
• Feb 9th 2009, 08:33 AM
elpermic
I am thinking that when t=0, C=10. Am I suppose to cancel out P to find out k or something?
• Feb 9th 2009, 12:20 PM
HallsofIvy
Quote:

Originally Posted by elpermic
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, $\displaystyle P= ^3\sqrt{2700t+ C}$.