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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 5EA
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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: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
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
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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