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## Homework Statement

"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.

## Homework Equations

## 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 :)

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