Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old), subadult (1 to 2 yrs), and adult (over 2 yrs old). They concluded that the change in the makeup of the bird population in successive years could be described by the matrix equation below. The numbers in the column matrices give the numbers of females in the three age groups after n years and n + 1 years. Note that j, is the number of juveniles, s, is the number of sub-adults, and a, is the number of adults at time n. b. Using advanced techniques from linear algebra, we can show that in the long run the following equation is true. In+ 1 In Sn+ 1 S0,98 S. an+1 an In + 1 Jn What can we conclude about the long-term fate of the birds? 0 0.32 O A. The population of the birds will grow exponentially. Sn+ 1 = 0.17 O B. The birds will become extinct. 0 0.73 0.94 an+ 1 O C. The population of the birds will decrease linearly. c. In the model, the main impediment to the survival of the bird is the number 0.17 in the second row of the 3 x3 matrix. Suppose that due to better forest management, the number 0.17 can be increased to 0.28. Rework part a under this new assumption. In the first year there will be female birds. (Do not round until the final answer. Then round to the nearest whole number as needed.)
Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old), subadult (1 to 2 yrs), and adult (over 2 yrs old). They concluded that the change in the makeup of the bird population in successive years could be described by the matrix equation below. The numbers in the column matrices give the numbers of females in the three age groups after n years and n + 1 years. Note that j, is the number of juveniles, s, is the number of sub-adults, and a, is the number of adults at time n. b. Using advanced techniques from linear algebra, we can show that in the long run the following equation is true. In+ 1 In Sn+ 1 S0,98 S. an+1 an In + 1 Jn What can we conclude about the long-term fate of the birds? 0 0.32 O A. The population of the birds will grow exponentially. Sn+ 1 = 0.17 O B. The birds will become extinct. 0 0.73 0.94 an+ 1 O C. The population of the birds will decrease linearly. c. In the model, the main impediment to the survival of the bird is the number 0.17 in the second row of the 3 x3 matrix. Suppose that due to better forest management, the number 0.17 can be increased to 0.28. Rework part a under this new assumption. In the first year there will be female birds. (Do not round until the final answer. Then round to the nearest whole number as needed.)
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 22CT
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Some ecologists divided a female bird population into three categories:
juvenile (up to 1 yr old), subadult (1 to 2 yrs), and adult (over 2 yrs old). They
concluded that the change in the makeup of the bird population in successive
years could be described by the matrix equation below. The numbers in the
column matrices give the numbers of females in the three age groups after n
years and n + 1 years. Note that j, is the number of juveniles, s, is th
b. Using advanced techniques from linear algebra, we can show that in the long run the following
equation is true.
Jn +1
In
80.98 Sn
Jn
number of sub-adults, and a, is the number of adults at time n.
Sn+ 1
an + 1
an
In + 1
0 0.32
Jn
What can we conclude about the long-term fate of the birds?
O A. The population of the birds will grow exponentially.
Sn+1
0.17
B. The birds will become extinct.
0 0.73 0.94
an + 1
an
O C. The population of the birds will decrease linearly.
c. In the model, the main impediment to the survival of the bird is the number 0.17 in the second row of
the 3x3 matrix. Suppose that due to better forest management, the number 0.17 can be increased to
0.28. Rework part a under this new assumption. In the first year there will be female birds.
(Do not round until the final answer. Then round to the nearest whole number as needed.)
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