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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(bd)t+HHe(bd)t(bd)dNdt=a(bd)e(bd)tH(bd)e(bd)tbddNdt=(bd)[ae(bd)tHe(bd)tbd]dNdt=(bd)[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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