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Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1 1.3 1.2 0.9 0 0 0 L = 0 0 0.6 0 0 0 0.2 0 and the initial population distribution is 42 of the first age group, 17 of the second age group, 11 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = Are the elk thriving, static, or going extinct?? (The growth rate is the percentage of growth over/under 100%.)

Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1 1.3 1.2 0.9 0 0 0 L = 0 0 0.6 0 0 0 0.2 0 and the initial population distribution is 42 of the first age group, 17 of the second age group, 11 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = Are the elk thriving, static, or going extinct?? (The growth rate is the percentage of growth over/under 100%.)

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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Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1 1.3 1.2 0.9 0 0 0 L = 0 0 0.6 0 0 0 0.2 0 and the initial population distribution is 42 of the first age group, 17 of the second age group, 11 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = Are the elk thriving, static, or going extinct?? (The growth rate is the percentage of growth over/under 100%.)
Transcribed Image Text:Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1 1.3 1.2 0.9 0 0 0 L = 0 0 0.6 0 0 0 0.2 0 and the initial population distribution is 42 of the first age group, 17 of the second age group, 11 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is x0 = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = Are the elk thriving, static, or going extinct?? (The growth rate is the percentage of growth over/under 100%.)
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