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

[musad]

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.
%

 

[pickslides]

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