population growth model

• March 27th 2006, 01:43 PM
charps43
population growth model
Having problems with a homework problem:

2 populations (J(t) and K(t)) of microbial species are each assumed to grow according to the euler differential equation model, with different growth parameters c and d, respectively. Suppose the populations are grown together in a beaker, and define p(t) = J(t) / (J(t) + K(t)) to be the fraction of the total population that is of species type J. Using differential equations for J and K, show that p(t) satisfies a logistic growth equation.

thanks,
charps
• March 27th 2006, 07:19 PM
charps43
coming down to the wire on this one. any help or hints would be awesome.

charps
• March 27th 2006, 07:23 PM
ThePerfectHacker
Maybe you can say,
$J(t)=Ae^{st}$
$K(t)=Be^{rt}$

Then, show that
$p'(t)=kp(t)$
Knowing that,
$p(t)=\frac{Ae^{st}}{Ae^{st}+Be^{rt}}$
• March 27th 2006, 08:38 PM
charps43
thank you.