It is more convenient to solve a single equation instead of both of (1, 2), if possible. Fortunately, since both sides of (1) are derivatives, it is dead easy to integrate this equation. Let the initial conditions be given as and , and integrate both sides of (1):

Notice that we have now solved for in terms of and known quantities. Substituting this result into (2) gives

Now, if we define

we get the standard ecological form of the logistic equation:

where is the intrinsic growth rate of this population for this density of sugar and is the carrying capacity of this sugar solution.

2000-07-31