Solving for K and Time when P=44 in Alligator Population Problem

[Eng67]

I am having a problem with finding the constant K in This problem.

The time rate of change of an alligator population P in a swamp is proportional to the square root of P. The swamp contains 9 alligators in 2000 and 25 alligators in 2005. When will there be 44 alligators in the swamp?

I have determined the formula dP/dT = KP^1/2

P(0)=9, P(5)=25

P^-1/2dP = Kdt and 2P^1/2=C + Kt

A simple push with how to introduce the values into this equation would be greatly appreciated.

 

[finchie_88]

If I'm not mistaken...
$$2\sqrt{p} = c + kt$$
if t = 0, then p = 9, and the kt term disappears, so you can get a value for C. Then do the same kind of thing for the value of k using the other piece of data you are given.

 

[HallsofIvy]

Two unknowns, C and K, so you need two equations. You are given two pieces of information. As finchie_88 suggested (although he didn't say it explicitely), let t be the number of years since 2000. Then when t= 0, P= 9 and when t= 5, P= 25. Put those numbers into your formula to get two equations for C and K.

 

[Eng67]

Thanks for the replies! It has become much clearer now.