
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.
any input would be helpful.
thanks,
charps

coming down to the wire on this one. any help or hints would be awesome.
charps

Maybe you can say,
$\displaystyle J(t)=Ae^{st}$
$\displaystyle K(t)=Be^{rt}$
Then, show that
$\displaystyle p'(t)=kp(t)$
Knowing that,
$\displaystyle p(t)=\frac{Ae^{st}}{Ae^{st}+Be^{rt}}$
