Because of the continued successful implementation of an urban renewal program, it is expected that each year 2% of the population currently residing in the city will move to the suburbs and 4% of the population currently residing in the suburbs will move into the city. If the initial probability distribution is
What will be the population distribution of the city after 1 year? After 2 years? Assume that the total population of the metropolitan area remains constant.

A) after 1 year: 69.8% in the city, 30.2% in the city after 2 yr: 68.1% in the city, 31.9% in the city
B) after 1 year: 69% in the city, 31% in the city after 2 yr: 69.612% in the city, 30.388% in the city
C) after 1 year: 69.8% in the city, 30.2% in the city after 2 yr: 69.612% in the city, 30.388% in the city
D) after 1 year: 69% in the city, 31% in the city after 2 yr: 68.1% in the city, 31.9% in the city

Question

Because of the continued successful implementation of an urban renewal program, it is expected that each year 2% of the population currently residing in the city will move to the suburbs and 4% of the population currently residing in the suburbs will move into the city. If the initial probability distribution is ​  ​
What will be the population distribution of the city after 1 year? After 2 years? Assume that the total population of the metropolitan area remains constant.
​
A) after 1 year: 69.8% in the city, 30.2% in the city after 2 yr: 68.1% in the city, 31.9% in the city ​ 
B) after 1 year: 69% in the city, 31% in the city after 2 yr: 69.612% in the city, 30.388% in the city ​ 
C) after 1 year: 69.8% in the city, 30.2% in the city after 2 yr: 69.612% in the city, 30.388% in the city ​ 
D) after 1 year: 69% in the city, 31% in the city after 2 yr: 68.1% in the city, 31.9% in the city ​

Quizplus · Accepted Answer

After 1 year: 
- 11% of the current population will still be in the city. 
- 2% of the current population in the city will move to the suburbs, so 0.02(89%) = 1.78% of the current total population will move from the city to the suburbs. 
- 4% of the current population in the suburbs will move to the city, so 0.04(11%) = 0.44% of the current total population will move from the suburbs to the city. 
Therefore, the population distribution in the city after 1 year will be 11% - 1.78% + 0.44% = 9.66%, and in the suburbs will be 89% + 1.78% - 0.44% = 90.34%.
After 2 years: 
- 9.66% of the population will be in the city. 
- 2% of the population in the city will move to the suburbs, so 0.02(90.34%) = 1.81% of the total population will move from the city to the suburbs. 
- 4% of the population in the suburbs will move to the city, so 0.04(9.66%) = 0.39% of the total population will move from the suburbs to the city. 
Therefore, the population distribution in the city after 2 years will be 9.66% - 1.81% + 0.39% = 8.24%, and in the suburbs will be 90.34% + 1.81% - 0.39% = 91.76%. 
The closest choice to this distribution is C, which has a population distribution of 69.8% in the city and 30.2% in the suburbs after 1 year, and a population distribution of 69.612% in the city and 30.388% in the suburbs after 2 years.

Because of the Continued Successful Implementation of an Urban Renewal