An ecologist is studying the impacts of air pollution on giant panda populations, specifically on anda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close o the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 4) 1 in 3 female baby pandas survive to become adult female pandas each year. 5) The population of giant pandas is balanced between the sexes (equivalent males and females) Model these population as two systems of linear equations that relates the current population (n) to what it will be after one year (n + 1). Part of each system has been provided for you. Fill in the coefficients according to the information above.
An ecologist is studying the impacts of air pollution on giant panda populations, specifically on anda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data from the last 30 years that allows her to fit two models to the evolution of giant panda populations over time (one for 30 years and one for the last 5 years after a new chemical plant was built close o the panda habitat). She will use these models to determine the long-term impacts of this pollution on panda populations. She has the following information to help her model the two sets of population dynamics data on adult and baby pandas : 1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are born each year (reproduction rate = 0.75). 2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born each year (reproduction rate = 0.7). 3) 3 in 4 of the adult female pandas survive to the next year. 4) 1 in 3 female baby pandas survive to become adult female pandas each year. 5) The population of giant pandas is balanced between the sexes (equivalent males and females) Model these population as two systems of linear equations that relates the current population (n) to what it will be after one year (n + 1). Part of each system has been provided for you. Fill in the coefficients according to the information above.
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:An ecologist is studying the impacts of air pollution on giant panda populations, specifically on
panda birth rates. Due to the historical interest in giant pandas, the ecologist has access to data
from the last 30 years that allows her to fit two models to the evolution of giant panda populations
over time (one for 30 years and one for the last 5 years after a new chemical plant was built close
to the panda habitat). She will use these models to determine the long-term impacts of this
pollution on panda populations. She has the following information to help her model the two sets
of population dynamics data on adult and baby pandas :
i.
1) Without pollution, for every 1 adult female panda a year earlier, 0.75 baby pandas are
born each year (reproduction rate = 0.75).
2) With pollution, for every 1 adult female panda a year earlier, 0.7 baby pandas are born
each year (reproduction rate = 0.7).
3) 3 in 4 of the adult female pandas survive to the next year.
1 in 3 female baby pandas survive to become adult female pandas each year.
The population of giant pandas is balanced between the sexes (equivalent males and
females)
4)
5)
Model these population as two systems of linear equations that relates the current
population (n) to what it will be after one year (n + 1). Part of each system has been
provided for you. Fill in the coefficients according to the information above.
With pollution (55):
bn+1
Antl
=
Without pollution ():
bn+1
antl =
=
bn +
bn +
bn +
bn +
an
an
an
an
Transcribed Image Text:i.
ii.
iii.
Find the dominant eigenvalue for each of these systems and estimate the corresponding
basic eigenvector for each.
With pollution :
Without pollution :
Describe the panda population in the long-run for both models .If numerical values can be
used to describe the relative populations, provide them.
What recommendations related to the pollution should our ecologist make based on these
results
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