(a) Your ancester Haopeng is famous for having studied rabbit and fox populations on an isolated...
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(a) Your ancester Haopeng is famous for having studied rabbit and fox populations on an isolated island in the Indian Ocean. They denoted the number of rabbits and foxes on the island in the 12-th month after they began their study by an and bn respectively and they observed that the populations followed a pattern given by. an+1 = 12.4an - 2.8bn and b1 = 4.2an +2.6bn. For the 100th aniversary of their work, you would like to modernise the mathematics in their study and decide to write this relationship in matrix form as an+1 bn+1 where B is a 2 x 2 matrix. Find B and enter it in the box below using Maple syntax. 1 Syntax advice: Use Maple syntax for matrices. For example, if your answer is 2 10 52 < <1, 10> | < 2, 52 > > or B where (i) Explain in the box below why < <12>, <10 | 52>> (b) More recently, on another isolated island, your friend Bhawan has been studying the rat and owl populations in a similar way and they denote by, and y, the numbers of rats and owls, respectively, on their island in the n-th month after their study began. Because of the prey-predator relation between the two species, Bhawan has observed that an In+1 In I^^^ ) = A (n), Yn+1 A 9.2 -2.4 3.6 (+) = 2.4). 0.8 = An (20). then enter (ii) Suppose that you are given and co = 245 and yo I5 = 3/5 = = lim n Yn A = - ( 3) (6 2) ( 70. Find the following values. (iii) Using the same values of owl populations, i.e., to find lim 245 and yo In n Yn = = 70 Bhawan would like to find the long term ratio of the rat and Help Bhawan by giving your answer in the box below. In END OF THIS QUESTION (a) Your ancester Haopeng is famous for having studied rabbit and fox populations on an isolated island in the Indian Ocean. They denoted the number of rabbits and foxes on the island in the 12-th month after they began their study by an and bn respectively and they observed that the populations followed a pattern given by. an+1 = 12.4an - 2.8bn and b1 = 4.2an +2.6bn. For the 100th aniversary of their work, you would like to modernise the mathematics in their study and decide to write this relationship in matrix form as an+1 bn+1 where B is a 2 x 2 matrix. Find B and enter it in the box below using Maple syntax. 1 Syntax advice: Use Maple syntax for matrices. For example, if your answer is 2 10 52 < <1, 10> | < 2, 52 > > or B where (i) Explain in the box below why < <12>, <10 | 52>> (b) More recently, on another isolated island, your friend Bhawan has been studying the rat and owl populations in a similar way and they denote by, and y, the numbers of rats and owls, respectively, on their island in the n-th month after their study began. Because of the prey-predator relation between the two species, Bhawan has observed that an In+1 In I^^^ ) = A (n), Yn+1 A 9.2 -2.4 3.6 (+) = 2.4). 0.8 = An (20). then enter (ii) Suppose that you are given and co = 245 and yo I5 = 3/5 = = lim n Yn A = - ( 3) (6 2) ( 70. Find the following values. (iii) Using the same values of owl populations, i.e., to find lim 245 and yo In n Yn = = 70 Bhawan would like to find the long term ratio of the rat and Help Bhawan by giving your answer in the box below. In END OF THIS QUESTION
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Posted Date:
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