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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Just a,b and e.
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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