MHB What is the long-term percentage of city dwellers?

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The discussion focuses on the movement of populations between urban and rural areas, specifically examining the long-term percentage of city dwellers. Each year, 20% of rural residents move to cities, while 10% of city residents relocate to rural areas. In 2015, 50% of the population lived in cities, with calculations showing that by 2016, this percentage would rise to 55%, and by 2017, it would reach 58.5%. The main question remains how to determine the long-term percentage of city dwellers using transition matrix logic. The conversation emphasizes the need for a mathematical approach to find a stable population distribution over time.
musad
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Hi, I am having trouble with the following question, I've answered part a but I am not sure about part b:

Suppose each year 20% of people who live in the country move into the city, while 10% of the city people move into the country.
a) If in 2015, 50% of the population live in the cities, what are the population percentages in
(i) 2016
Pcountry= 45%


Pcity= 55%


(ii) 2017
Pcountry= 41.5%


Pcity= 58.5%

b) Find the long-term percentage of city dwellers.
%



 
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Use the same logic as explained here:http://mathhelpboards.com/advanced-probability-statistics-19/transition-matrix-question-14207.html#post67359
 

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