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2.2.12. A forest is composed of two species of trees, A and B. Each year of the trees of species A are replaced by trees of species B, while i of the trees of species B are replaced by trees of species A. The remaining trees either survive or are replaced by trees of their own species. a. Letting A, and B, denote the number of trees of each type in year t, give equations for A+1 and B1+1 in terms of A, and B1. b. Write the equations of part (a) as a single matrix equation.

2.2.12. A forest is composed of two species of trees, A and B. Each year of the trees of species A are replaced by trees of species B, while i of the trees of species B are replaced by trees of species A. The remaining trees either survive or are replaced by trees of their own species. a. Letting A, and B, denote the number of trees of each type in year t, give equations for A+1 and B1+1 in terms of A, and B1. b. Write the equations of part (a) as a single matrix equation.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 58PPS
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2.2.12. A forest is composed of two species of trees, A and B. Each year of the trees of species A are replaced by trees of species B, while i of the trees of species B are replaced by trees of species A. The remaining trees either survive or are replaced by trees of their own species. a. Letting A, and B, denote the number of trees of each type in year t, give equations for A+1 and B1+1 in terms of A; and B,. b. Write the equations of part (a) as a single matrix equation. c. Use part (b) to get a formula for A,+2 and B,+2 in terms of A, and B. d. Use part (b) to get a formula for A,–1 and B,–1 in terms of A, and Br. = 100. By hand, calculate A, and B¡ for e. Suppose Ao t = 1, 2, and3. Use MATLAB to check your work and extend the calculation through t = 10. What is happening to the populations? = 100 and Bo
Transcribed Image Text:2.2.12. A forest is composed of two species of trees, A and B. Each year of the trees of species A are replaced by trees of species B, while i of the trees of species B are replaced by trees of species A. The remaining trees either survive or are replaced by trees of their own species. a. Letting A, and B, denote the number of trees of each type in year t, give equations for A+1 and B1+1 in terms of A; and B,. b. Write the equations of part (a) as a single matrix equation. c. Use part (b) to get a formula for A,+2 and B,+2 in terms of A, and B. d. Use part (b) to get a formula for A,–1 and B,–1 in terms of A, and Br. = 100. By hand, calculate A, and B¡ for e. Suppose Ao t = 1, 2, and3. Use MATLAB to check your work and extend the calculation through t = 10. What is happening to the populations? = 100 and Bo
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