Science:Math Exam Resources/Courses/MATH102/December 2019/Question 08(a)/Statement

The Allee effect is a phenomenon in ecology by which the per capita reproduction rate of the population increases with increasing population density. In Canada the Allee effect can be observed in the Atlantic cod population in the Gulf of St.Lawrence, where cod is the preferred prey of grey seals. A simple model of the Atlantic cod population growth rate is a modified logistic equation:

$\displaystyle f(N)=N({\frac {N}{2}}-1)(1-N)$

where N is measured in millions of kg of fish. We can assume $N\geq 0.$

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(4 points) Sketch the function f(N) for $N\geq 0$. Include the N-values of any roots, extrema, inflection points, and horizontal asymptotes of the function f(N), should they exits. Make sure your graph is big enough to clearly show all intersecting points.