What is the long-term percentage of city dwellers?

In summary, a transition matrix problem is a mathematical problem used to model the behavior of a system over time. It involves creating a matrix that shows the probabilities of transitioning from one state to another in a given time step. These problems are commonly used in scientific research to understand the behavior of complex systems and make predictions. The key components of a transition matrix are the states of the system, the transition probabilities between states, and the time step. This type of problem can have multiple solutions depending on the initial conditions and transition probabilities, and it has many real-world applications in fields such as biology, economics, and computer science.
  • #1
musad
8
0
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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  • #2
Use the same logic as explained here:http://mathhelpboards.com/advanced-probability-statistics-19/transition-matrix-question-14207.html#post67359
 

FAQ: What is the long-term percentage of city dwellers?

What is a transition matrix problem?

A transition matrix problem is a mathematical problem used to model the behavior of a system over time. It involves creating a matrix that shows the probabilities of transitioning from one state to another in a given time step.

How is a transition matrix problem used in scientific research?

Transition matrix problems are commonly used in fields such as biology, economics, and computer science to understand the behavior of complex systems. They can also be used to make predictions and analyze trends.

What are the key components of a transition matrix?

The key components of a transition matrix are the states of the system, the transition probabilities between states, and the time step in which these transitions occur.

Can a transition matrix problem have multiple solutions?

Yes, a transition matrix problem can have multiple solutions depending on the initial conditions and the transition probabilities. In some cases, there may be more than one stable equilibrium state.

What are some real-world applications of transition matrix problems?

Transition matrix problems are used in a variety of real-world applications, such as population dynamics, stock market analysis, and predicting the spread of diseases. They are also used in machine learning algorithms and natural language processing.

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