ODE Logistics Equation: Solving for Rabbit Population Growth Rate

[cue928]

I have the following logistics problem that I am stuck about halfway thru:
The time rate of change of a rabbit population P is proportional to the square root of P. At time t=0 (months) the population numbers 100 rabbits and is increasing at the rate of 20 rabbits per month. How many rabbits will there be one year late?

I obtained the equation dy/dt = k*p^.5 I solved for a "k" value of 2, but I do not know where to go from there. How do I account for the 20? I understand that is a rate of change but at what point do you substitute that in the problem?

 

[2h2o]

You already used the 20(=dP/dt @ t=0) to find your rate constant (k).

Next step (actually, the first step I did when working through it) is to find the value of the constant of integration you get when you integrate to find your unknown function. Use the given initial conditions P(0)=100.