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The Leslie matrix below describes a population with four age groups consisting of juveniles, subadults, young adults, and mature adults. The initial population at time 0 is given by X(0). [0.8 1 2.5 21 50 0.5 40 L = and X(0) = 0.6 78 0.7 0 70 (a) What is the percentage of juveniles in the initial population? Round your answer to 2 decimal places. Answer = (b) If the largest eigenvalue of L is c = 1.31, what is true about the long-term fate of this population? The population dies out because the initial population is an eigenvector The population stays the same because the initial population is not an eigenvector The population grows exponentially because the long-term growth rate c is positive The population dies out because the long-term growth rate c is less than 1 O The population grows exponentially because the long-term growth rate c is greater than 1

The Leslie matrix below describes a population with four age groups consisting of juveniles, subadults, young adults, and mature adults. The initial population at time 0 is given by X(0). [0.8 1 2.5 21 50 0.5 40 L = and X(0) = 0.6 78 0.7 0 70 (a) What is the percentage of juveniles in the initial population? Round your answer to 2 decimal places. Answer = (b) If the largest eigenvalue of L is c = 1.31, what is true about the long-term fate of this population? The population dies out because the initial population is an eigenvector The population stays the same because the initial population is not an eigenvector The population grows exponentially because the long-term growth rate c is positive The population dies out because the long-term growth rate c is less than 1 O The population grows exponentially because the long-term growth rate c is greater than 1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 41EQ
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The Leslie matrix below describes a population with four age groups consisting of juveniles, subadults, young adults, and mature adults. The initial population at time 0 is given by X(0). 0.8 1 2.5 2 50 0.5 40 L = and X(0) = 0.6 78 0.7 0] 70 (a) What is the percentage of juveniles in the initial population? Round your answer to 2 decimal places. Answer = (b) If the largest eigenvalue of L is c= 1.31, what is true about the long-term fate of this population? The population dies out because the initial population is an eigenvector The population stays the same because the initial population is not an eigenvector The population grows exponentially because the long-term growth rate c is positive The population dies out because the long-term growth rate c is less than 1 The population grows exponentially because the long-term growth rate c is greater than 1
Transcribed Image Text:The Leslie matrix below describes a population with four age groups consisting of juveniles, subadults, young adults, and mature adults. The initial population at time 0 is given by X(0). 0.8 1 2.5 2 50 0.5 40 L = and X(0) = 0.6 78 0.7 0] 70 (a) What is the percentage of juveniles in the initial population? Round your answer to 2 decimal places. Answer = (b) If the largest eigenvalue of L is c= 1.31, what is true about the long-term fate of this population? The population dies out because the initial population is an eigenvector The population stays the same because the initial population is not an eigenvector The population grows exponentially because the long-term growth rate c is positive The population dies out because the long-term growth rate c is less than 1 The population grows exponentially because the long-term growth rate c is greater than 1
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