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The model in equation (1) in part a describes a population untouched by humans there is no harvesting. We can model what happens if harvest H individuals from the population each period. The unlimited population growth with harvesting model is given by

 

N(t) = ae^(b-d)t +H - He^(b-d)t/(b-d) 

 

where b is the birth rate and d is the death rate and h is the number of individuals taken from the population in each period 

 

Show that the rate of population change is :

dn(t)/dt = (b-d)*N(t) -H

 Jun 4, 2019
 #1
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N(t) = ae^(b-d)t +H - He^(b-d)t/(b-d) 

 

\(N(t) = ae^{(b-d)t} +H - \frac{He^{(b-d)t}}{(b-d)}\\ \frac{dN}{dt} =a(b-d)e^{(b-d)t}-\frac{H(b-d)e^{(b-d)t}}{b-d}\\ \frac{dN}{dt} =(b-d)[ae^{(b-d)t}-\frac{He^{(b-d)t}}{b-d}]\\ \frac{dN}{dt} =(b-d)[N(t)-H]\\ \)

 

Which is differnet from what you wanted but I think you forgot to include some brackets.   wink

 Jun 7, 2019

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