Hello, I am having trouble solving this problem exactly. I used a 20 population difference both ways at t=1 and t= -1 to approximate the answer but it is still not right. The answer is 484 rabbits after 12 months.

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 month later?

I base my equation on the standard dP/dt=(B-D)k*P^(1/2) where B is the birth rate and D is the death rate at t=0. I solved that to find

P(t)=(kt+(P_0)^(1/2))^(2).

The problem is that I know I can't assume that at t=1 The birth rate is still 20.

Thank you