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# hw 6 - Calculus for the Life Science I MAT1330A MAT1330B...

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Calculus for the Life Science I MAT1330A , MAT1330B, MAT1330E Assignment 6 Due date: Oct. 28 Instructor (circle one): Jing Li , Catalin Rada , Frithjof Lutscher DGD (circle one): 1 , 2 , 3 , 4 Student Name (printed): Student ID Number: Question 1 An animal species is described by the discrete dynamical system N i +1 = 1 . 5 N i (1 - N i ) - hN i , i = 0 , 1 , 2 , 3 , . . . , where N i is the fraction of the maximal population after i years. h is the harvesting effort of the predators. a ) Find the equilibrium points. One of these points will depend of h . Equilibrium points : b ) Given the largest interval for h such that the equilibrium points in ( a ) have a biological meaning. Interval for h : c ) Find the equilibrium harvest R for this species as a function of h . R = d ) Determine the harvesting effort h that will maximize the equilibrium harvest. h = e ) Give the maximal equilibrium harvest. R = f ) Is the maximal equilibrium harvest stable or unstable ? The maximal equilibrium harvest is (circle one) stable or unstable because .

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