# Birth and death rates of roaches.

1. Jan 19, 2014

### cp255

1. The problem statement, all variables and given/known data

Consider a population model in which the birth and death rates and  of a cockroach
population P are both proportional to sqrt(P). (Recall that in a “normal” exponential growth
model, B and  D are constants.) If the cockroach population has increased from 100 to 400
in one week, what will the population be in another week? Is this model reasonable?

2. Relevant equations

3. The attempt at a solution

So I am not sure exactly how to model this. Here is my attempt but I think it is wrong since there are too many unknowns for the information given.

B = k*sqrt(P)
D = w*sqrt(P)

Where B is the birth rate, D is the death rate, and they are both equal to different constants multiplied by the square root of P.

So here is the differential equation I cam up with...
dP/dt = (k*sqrt(P) - w*sqrt(P))P

However I think there are too many unknowns for the information given.

2. Jan 20, 2014

### Office_Shredder

Staff Emeritus
If you do a little algebra
$$\frac{dP}{dt} = (k-w) P^{3/2}$$
Now it doesn't matter what k and w are, just what k-w is. So you really only have one unknown that matters.