consider an animal population P(t) with constant death rate 0.02 (deaths per animal per month) and with birth rate proportional to P. suppose that P(0)=200 and P'(0)=2. when is P=1000?

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- Jul 12th 2012, 12:06 PMmath254population problem
consider an animal population P(t) with constant death rate 0.02 (deaths per animal per month) and with birth rate proportional to P. suppose that P(0)=200 and P'(0)=2. when is P=1000?

- Jul 13th 2012, 01:51 PMtom@ballooncalculusRe: population problemQuote:

constant death rate 0.02 (deaths per animal per month)

Quote:

and with birth rate proportional to P.

And with...

$\displaystyle \frac{dP}{dt} = B - D$

... we have...

$\displaystyle \frac{dP}{dt} = kP - \frac{1}{5}$

... which is suitably arranged as either...

$\displaystyle \frac{1}{kP - \frac{1}{5}}\ k\ \frac{dP}{dt} = k$

... or else...

$\displaystyle \frac{dP}{dt} - kP = - \frac{1}{5}$

... according to taste.

Just in case a picture helps...

http://www.ballooncalculus.org/draw/factor/pop.png

... where (key in spoiler) ...

__Spoiler__:

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