We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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

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

5 Online Users