Thanks for reading this... I've got my midterm tomorrow and I just want to make sure I know every nook and cranny of the review sheet... Here's the problem:
A population of goldfish in a certain pond is modelled by:
dG/dt = G*(1-6/30)*(1-200/G)*(1-300/G)
where G is the number of goldfish in the pond. Identify equilibrium points and their stability. If there are initially 17 goldfish in the pond, what is the ultimate fate of their population? Note: you DO NOT have to actually solve this differential equation.
I found the equilibrium points to be G=0, 30, 200, and 300. After drawing a phase diagram and plugging in numbers to the equation, I found that G=0 and G=200 are unstable, and G=30 and G=300 are stable. However, I cannot figure out how I am supposed to find the fate of the population without solving the DE... Can somebody point me in the right direction?
Thanks in advance,