Suppose the population of a particular endangered bird changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30 Suppose also that the yearly transition matrix is 60 breeding adults, that is Xo = 30 A [0 1.25] S 0.5 where s is the proportion of chicks that survive to become adults (note that 0 < s < 1 must be true because of what this number represents). (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? (b) Scientists are concerned that the species may become extinct. Explain why if 0 < s < 0.4 the species will become extinct. (c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will this size be?
Suppose the population of a particular endangered bird changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30 Suppose also that the yearly transition matrix is 60 breeding adults, that is Xo = 30 A [0 1.25] S 0.5 where s is the proportion of chicks that survive to become adults (note that 0 < s < 1 must be true because of what this number represents). (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? (b) Scientists are concerned that the species may become extinct. Explain why if 0 < s < 0.4 the species will become extinct. (c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will this size be?
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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![Suppose the population of a particular endangered bird changes on a yearly basis as
a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30
Suppose also that the yearly transition matrix is
[60]
breeding adults, that is xo
=
30
[0 1.25]
A
[
where s is the proportion of chicks that survive to become adults (note
S
0.5
that 0< s < 1 must be true because of what this number represents).
(a) Which entry in the transition matrix gives the annual birthrate of chicks per adult?
(b) Scientists are concerned that the species may become extinct. Explain why if 0 <
s < 0.4 the species will become extinct.
(c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will
this size be?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dc2cca1-10d2-4771-9915-55688e05ff2a%2Fd49adf2d-f285-44b2-9936-fdfa86b0e456%2F59njakn_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose the population of a particular endangered bird changes on a yearly basis as
a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30
Suppose also that the yearly transition matrix is
[60]
breeding adults, that is xo
=
30
[0 1.25]
A
[
where s is the proportion of chicks that survive to become adults (note
S
0.5
that 0< s < 1 must be true because of what this number represents).
(a) Which entry in the transition matrix gives the annual birthrate of chicks per adult?
(b) Scientists are concerned that the species may become extinct. Explain why if 0 <
s < 0.4 the species will become extinct.
(c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will
this size be?
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