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# hw 1 soln - Calculus for the Life Science I MAT1330A...

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Calculus for the Life Science I MAT1330A , MAT1330B, MAT1330E Assignment 1 Due date: Sept. 23 Instructor (circle one): Jing Li , Catalin Rada , Frithjof Lutscher DGD (circle one): 1 , 2 , 3 , 4 Student Name (printed): Student ID Number: Question 1 The size of a bird population on an island located close to the cost of Newfoundland depends on the local growth rate (birth minus death) and the migration between the island and New- foundland. A discrete dynamical system modelling this population is x n +1 = 0 . 85 x n + 75 , n = 0 , 1 , 2 , 3 , . . ., where x n is the size of the bird population on the island after n years. 0 . 85 is the local growth rate and 75 is the yearly increase due to migration. a ) If x 0 = 200, then x 1 = 245 , x 2 = 283.25 , x 3 = 315.7625 b ) Give the updating function f of the dynamical system. f ( x ) = 0 . 85 x + 75 c ) Find the equilibrium point p of the dynamical system. p = 500 p = 0 . 85 p + 75 p - 0 . 85 p = 75 0 . 15 p = 75 p = 75 / 0 . 15 = 500 . d

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hw 1 soln - Calculus for the Life Science I MAT1330A...

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