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Ithryndil
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Homework Statement
A certain bacterium, given plenty of nutrient and room, is known to grow according to the Malthusian model with reproductive rate r. Suppose that the biologist working with the culture harvests the bacteria at a constant rate of h bacteria per hour. Use qualitative analysis to discuss the fate of the culture.
Homework Equations
[tex] P(t) = P_{0}e^{rt}[/tex]
The Attempt at a Solution
I have added [tex] P(t) = P_{0}e^{rt} - h*t[/tex] to my calculator and picked some values, however they don't match with the answer in the back of the book. I am wanting help understanding the answer in the back...The answer makes sense...but I can't figure out why...
The answer in the back of the book is:
The long-time activity of the population depends entirely on the sign of P(0) - (h/r). If it is negative, then the population will die out. If it is positive, the population will grow exponentially. If it is zero, then the population will remain at a constant (h/r).
Like I said, the answer makes some sense, however, I can't figure out why. Any help with the why is greatly appreciated. Thanks.