"The very simple population model for a resource limited population with constant immigration, and no breeding, M'(t) = M(S-M) + I attempts to describe the growth of corals on a reef. Function M(t) represents the biomass of corals."
a - Explain which term gives the immigration of juveniles onto the reef.
b - Describe the presumptions being made about the growth rate of corals at their different ages and sizes.
c - Determine if the biomass of corals tends to a limiting amount as [tex]t \rightarrow \infty[/tex] .
d - Suppose a coral reef has completely died, due to excessive cyanide fishing. Find and describe what this model suggests will be the pattern of its recovery.
The Attempt at a Solution
a - Is the immigration denoted as "I", because as immigration is constant, the I has 'constant effects' on the equation?
b - Is it correct to presume that the growth rate of the corals are constant, irregardless of their age and size?
c - I can see that its a first order non linear differential equation. But where do I go with this?
d - a regrowth rate represented by a logarithmic function?
The total marks for the 4 questions is 5 marks - if that helps
Thanks to all help received :)