Exponents and Natural Logarithms... interesting problem

From: Danuta (fuzzy_1207_at_hotmail.com)
Date: 12/31/04 

Date: Fri, 31 Dec 2004 03:36:13 +0000 (UTC)

Assume that a fish population grows according to the equation:
p = m/(1+ ae^-kt)

p is the initial population (1000 fish), m is the carrying capacity of the pond (25408.78378 fish maximum), k is 0.9, and t is the number od years.

Determine a ... i got 24.40878378.

Now using what you know, how many years will it take for the pond to reach it's carrying capacity?

This is tricky, because the way this is worded you don't really know what the equation is giving you... is p always equal to the initial amount or does that only serve to determine the value of the constant "a"

Good luck, and please help me with this, it's been really bugging me considering I have to get this done over Christmas break which is not thrilling for a 16 year old at all.