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Solved: A herd of American buffalo (bison) can be modeled

Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay ISBN: 9780321385178 62

Solution for problem 18E Chapter 5.6

Linear Algebra and Its Applications | 4th Edition

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Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay

Linear Algebra and Its Applications | 4th Edition

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Problem 18E

A herd of American buffalo (bison) can be modeled by a stage matrix similar to that for the spotted owls. The females can be divided into calves (up to 1 year old), yearlings (1 to 2 years), and adults. Suppose an average of 42 female calves are born each year per 100 adult females. (Only adults produce offspring.) Each year, about 60% of the calves survive, 75% of the yearlings survive, and 95% of the adults survive.For xk = ( ck , yk , ak ), where the entries in xk are the numbers of females in each life stage at year k.a. Construct the stage-matrix A for the buffalo herd, such that xk + 1 = Axk for k b. [M] Show that the buffalo herd is growing, determine the expected growth rate after many years, and give the expected numbers of calves and yearlings present per 100 adults.

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Chapter 5.6, Problem 18E is Solved
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Textbook: Linear Algebra and Its Applications
Edition: 4
Author: David C. Lay
ISBN: 9780321385178

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Solved: A herd of American buffalo (bison) can be modeled