Construct a stage-matrix model for an animal species that has two life stages: juvenile (up to 1 year old) and adult. Suppose the female adults give birth each year to an average of 1.6 female juveniles. Each year, 30% of the juveniles survive to become adults and 80% of the adults survive. For k ≥ 0,
Construct a stage-matrix model for an animal species that has two life stages: juvenile (up to 1 year old) and adult. Suppose the female adults give birth each year to an average of 1.6 female juveniles. Each year, 30% of the juveniles survive to become adults and 80% of the adults survive. For k ≥ 0,
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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Transcribed Image Text:let Xk =
(jk, ak), where the entries in X are the numbers of
female juveniles and female adults in year k.
a. Construct the stage-matrix A such that Xk+1 = Axk for
k ≥ 0.
b. Show that the population is growing, compute the eventual
growth rate of the population, and give the eventual ratio
of juveniles to adults.
c. Suppose that initially there are 15 juveniles and 10 adults
in the population. Produce four graphs that show how the
population changes over eight years: (a) the number of ju-
veniles, (b) the number of adults, (c) the total population,
and (d) the ratio of juveniles to adults (each year). When
does the ratio in (d) seem to stabilize? Include a listing of
the program or keystrokes used to produce the graphs for
(c) and (d).
Transcribed Image Text:17. Construct a stage-matrix model for an animal species that has
two life stages: juvenile (up to 1 year old) and adult. Suppose
the female adults give birth each year to an average of 1.6
female juveniles. Each year, 30% of the juveniles survive
to become adults and 80% of the adults survive. For k ≥ 0,
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