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@SithsAndGiggles heres a picture of the assignment if it make any difference. I have completed everything except #3

Its the first one, but the questions is to show that this equation has the same phase portrait as the equation from wiki

Here are some sample solutions for the example.|dw:1444188408781:dw|

|dw:1444189228506:dw| would it look like this

You have three equilibrium points, and so there are four intervals you should be considering: (1) \(y>K\), (2) \(A

Sorry, replace \(y\) with \(N\) in that last comment.
So let's say \(N<0\), in particular \(N=-1\). Then
\[\frac{dN}{dt}=r(-1)\left( -\frac{1}{A}-1\right)\left(1+\frac{1}{K}\right)\]
It looks like \(r\) is a positive constant, so keep that in mind. Since \(A\) is a positive number, the term \(-\dfrac{1}{A}-1\) is also negative. This multiplied by \(-1\) gives a positive number. Multiplied by \(r\), it's still positive. And since \(K>0\), \(1+\dfrac{1}{K}\) is too, and positive times positive is positive.
Now let's say \(0