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Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following example that looks at the population of an isolated colony of female beetles. Assume that the beetles live at most four years, we can divide them into four age groups (0-1, 1-2, 2-3, 3-4). Suppose that the initial population of 100 beetles (at year 1) records 30, 35, 25, 10 individuals for each corresponding group. Suppose that the birthrates for each of the groups are 0, 4, 2, and 1 per year. That is, beetles do not produce any young female in the first year of life, and they produce one young female in the fourth year. Suppose that the survival rate for each class is given by 0.7, 0.5, 0.2,0. A way to express the population at year 2 for each age group is the following: 4 1 30 0.7 35 0.5 25 0.2 0 10, Explain in words why the population of beetles at year 2 should be given by the above matrix multiplication.

Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following example that looks at the population of an isolated colony of female beetles. Assume that the beetles live at most four years, we can divide them into four age groups (0-1, 1-2, 2-3, 3-4). Suppose that the initial population of 100 beetles (at year 1) records 30, 35, 25, 10 individuals for each corresponding group. Suppose that the birthrates for each of the groups are 0, 4, 2, and 1 per year. That is, beetles do not produce any young female in the first year of life, and they produce one young female in the fourth year. Suppose that the survival rate for each class is given by 0.7, 0.5, 0.2,0. A way to express the population at year 2 for each age group is the following: 4 1 30 0.7 35 0.5 25 0.2 0 10, Explain in words why the population of beetles at year 2 should be given by the above matrix multiplication.

Advanced Engineering Mathematics
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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Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following example that looks at the population of an isolated colony of female beetles. Assume that the beetles live at most four years, we can divide them into four age groups (0-1, 1-2, 2-3, 3-4). Suppose that the initial population of 100 beetles (at year 1) records 30, 35, 25, 10 individuals for each corresponding group. Suppose that the birthrates for each of the groups are 0, 4, 2, and 1 per year. That is, beetles do not produce any young female in the first year of life, and they produce one young female in the fourth year. Suppose that the survival rate for each class is given by 0.7, 0.5, 0.2,0. A way to express the population at year 2 for each age group is the following: 4 1 30 0.7 35 0.5 25 0.2 0 10, Explain in words why the population of beetles at year 2 should be given by the above matrix multiplication.
Transcribed Image Text:Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following example that looks at the population of an isolated colony of female beetles. Assume that the beetles live at most four years, we can divide them into four age groups (0-1, 1-2, 2-3, 3-4). Suppose that the initial population of 100 beetles (at year 1) records 30, 35, 25, 10 individuals for each corresponding group. Suppose that the birthrates for each of the groups are 0, 4, 2, and 1 per year. That is, beetles do not produce any young female in the first year of life, and they produce one young female in the fourth year. Suppose that the survival rate for each class is given by 0.7, 0.5, 0.2,0. A way to express the population at year 2 for each age group is the following: 4 1 30 0.7 35 0.5 25 0.2 0 10, Explain in words why the population of beetles at year 2 should be given by the above matrix multiplication.
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