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February 5th, 2014, 04:02 PM   #1
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Population modeling

I'm stuck doing a question about population modeling. Specifically I've been given a growth rate and been asked to explain why it's suitable. For a population of initial size N at t=0 there is a constant death rate=D. The birth rate is initially B but decays to D over time. The overall growth rate when t=T for a constant T is one half its value.

Why is this model suitable:
Growth rate=(G*T^2)/(T^2+t^2)
where G=B-D

I get why that is suitable after plotting it out. At t=0 then growth rate is indeed=B-D as it would be and that the 1/t^2 term will create a decay of half every T. However its like 4 marks and I have no idea how to solve it beyond that. I'm not even sure If i need to say where it comes from but if I don't the explantion better be pretty good.
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