Consider the table below, giving the birth and death rates by age group for a population of small woodlands animals, where the age ranges are given in months. 0-3 3-6 6-9 9-12 12-15 0 0.3 0.8 0.7 0.4 Death rate () 0.4 0.1 0.1 0.2 0.4 Birth rate (A) 15-18 0 1 (a) What is the average life expectancy for one of the animals? (b) If the current population is distributed as below, what will be the distribution be in 1 month? 6 months? 1 year? 20 years? 0-3 3-6 6-9 9-12 12-15 15-18 Population 14 8 12 4 2 1 (c) What is the long-term population grow rate of the population? (d) What is the long-term age distribution (as percentage of total population) of the animals?
Consider the table below, giving the birth and death rates by age group for a population of small woodlands animals, where the age ranges are given in months. 0-3 3-6 6-9 9-12 12-15 0 0.3 0.8 0.7 0.4 Death rate () 0.4 0.1 0.1 0.2 0.4 Birth rate (A) 15-18 0 1 (a) What is the average life expectancy for one of the animals? (b) If the current population is distributed as below, what will be the distribution be in 1 month? 6 months? 1 year? 20 years? 0-3 3-6 6-9 9-12 12-15 15-18 Population 14 8 12 4 2 1 (c) What is the long-term population grow rate of the population? (d) What is the long-term age distribution (as percentage of total population) of the animals?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Transcribed Image Text:Consider the table below, giving the birth and death rates by age group for a population of small
woodlands animals, where the age ranges are given in months.
15-18
0-3 3-6 6-9 9-12 12-15
Birth rate (A) 0 0.3 0.8 0.7
Death rate () 0.4 0.1 0.1 0.2
0.4
0
0.4
1
(a) What is the average life expectancy for one of the animals?
(b) If the current population is distributed as below, what will be the distribution be in 1 month? 6
months? 1 year? 20 years?
0-3 3-6 6-9 9-12 12-15 15-18
Population 14 8 12 4
2
1
(c) What is the long-term population growth rate of the population?
(d) What is the long-term age distribution (as percentage of total population) of the animals?
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