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JATOT Question 1 (5 points) A MO12REV The government's investments in infrastructure combined with opportunities to work online is boosting the repopulation of villages in remote mountainous areas. The village Redrock had 1000 inhabitants on January 1", 2020. By January 1", 2025, this number of inhabitants is expected to double. Denote by N the number of inhabitants and by t the time in years from January 1st, 2020. a) Assuming that the population growth is linear, when will there be 4000 inhabitants? b) Assuming that the population growth is exponential, when will there be 4000 inhabitants? c) Assume that the maximum number of inhabitants the village can house is 10 000 and in the long term, the population will approach this maximum. The population growth is now assumed logistic, i.e. modeled by an equation of the form N = a with parameters a, b, c > 0. 1+e-b(t-c) When will there be 4000 inhabitants? d) Find the average growth rate for the population between January 1, 2020 and January 1st, 2025, for each of the three population growth models in a), b) and c).

JATOT Question 1 (5 points) A MO12REV The government's investments in infrastructure combined with opportunities to work online is boosting the repopulation of villages in remote mountainous areas. The village Redrock had 1000 inhabitants on January 1", 2020. By January 1", 2025, this number of inhabitants is expected to double. Denote by N the number of inhabitants and by t the time in years from January 1st, 2020. a) Assuming that the population growth is linear, when will there be 4000 inhabitants? b) Assuming that the population growth is exponential, when will there be 4000 inhabitants? c) Assume that the maximum number of inhabitants the village can house is 10 000 and in the long term, the population will approach this maximum. The population growth is now assumed logistic, i.e. modeled by an equation of the form N = a with parameters a, b, c > 0. 1+e-b(t-c) When will there be 4000 inhabitants? d) Find the average growth rate for the population between January 1, 2020 and January 1st, 2025, for each of the three population growth models in a), b) and c).

Advanced Engineering Mathematics
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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JATOT Question 1 (5 points) A MO12REV The government's investments in infrastructure combined with opportunities to work online is boosting the repopulation of villages in remote mountainous areas. The village Redrock had 1000 inhabitants on January 1", 2020. By January 1", 2025, this number of inhabitants is expected to double. Denote by N the number of inhabitants and by t the time in years from January 1st, 2020. a) Assuming that the population growth is linear, when will there be 4000 inhabitants? b) Assuming that the population growth is exponential, when will there be 4000 inhabitants? c) Assume that the maximum number of inhabitants the village can house is 10 000 and in the long term, the population will approach this maximum. The population growth is now assumed logistic, i.e. modeled by an equation of the form N = a with parameters a, b, c > 0. 1+e-b(t-c) When will there be 4000 inhabitants? d) Find the average growth rate for the population between January 1, 2020 and January 1st, 2025, for each of the three population growth models in a), b) and c).
Transcribed Image Text:JATOT Question 1 (5 points) A MO12REV The government's investments in infrastructure combined with opportunities to work online is boosting the repopulation of villages in remote mountainous areas. The village Redrock had 1000 inhabitants on January 1", 2020. By January 1", 2025, this number of inhabitants is expected to double. Denote by N the number of inhabitants and by t the time in years from January 1st, 2020. a) Assuming that the population growth is linear, when will there be 4000 inhabitants? b) Assuming that the population growth is exponential, when will there be 4000 inhabitants? c) Assume that the maximum number of inhabitants the village can house is 10 000 and in the long term, the population will approach this maximum. The population growth is now assumed logistic, i.e. modeled by an equation of the form N = a with parameters a, b, c > 0. 1+e-b(t-c) When will there be 4000 inhabitants? d) Find the average growth rate for the population between January 1, 2020 and January 1st, 2025, for each of the three population growth models in a), b) and c).
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