1The land of Zoo Nearland consists of two islands, the Each year 35% of the populatiou of the East Island moves to the West Island, and 25% of the population of the West Island moves to the East Island. Assume that the popaiations of the islands do not change for any other reason. (a) Let e. u be the populations of the East and West Islands, respectively. Firad expressions for e+i and wk+1 in terms of e and w. and hence find a differvnce equation X+i = Ax for X = htren mil

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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4. The land of Zoo Nearland consists of t wo islands, the East Island and the West sland.
Each year 35% of the populatiou of the East Island moves to the West Island, and 2% of
the populationm of the West Island moves to the East Island. Assume that the popaiations
of the islands do not change for any other reason.
(a) Let e. u be the populations of the East and West Islands, respectively. Feal
expressions for e+i and wh+1 in terms of c and w, and hence find a differvoce
equation X+1
Ax for x =
(b) Find the solution to the difference equation if there are initially eighteen million
people on each island.
(c) What is the population of cach island in the limit as k oc?
Transcribed Image Text:4. The land of Zoo Nearland consists of t wo islands, the East Island and the West sland. Each year 35% of the populatiou of the East Island moves to the West Island, and 2% of the populationm of the West Island moves to the East Island. Assume that the popaiations of the islands do not change for any other reason. (a) Let e. u be the populations of the East and West Islands, respectively. Feal expressions for e+i and wh+1 in terms of c and w, and hence find a differvoce equation X+1 Ax for x = (b) Find the solution to the difference equation if there are initially eighteen million people on each island. (c) What is the population of cach island in the limit as k oc?
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