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
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 22CT
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe22abc13-975e-4970-8f9b-505f9967ae15%2Fb8878677-79c7-41f3-93c7-79b5129cb97d%2Fdcdsmf8_processed.jpeg&w=3840&q=75)
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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