Chapter 2, Problem 12RP

Explanation of Solution

Relating two vectors:

Suppose that $R_t$ be the number of rural residents at the beginning of the year $t$, and $C_t$ be the number of city residents at the beginning of the year $t$.

Since 10% of the rural residents moved to city, remaining 90% of the rural decided to continue to stay at the rural residents at the beginning of the year t+1.

Thus, the number of rural residents in the beginning of the year t+1 is given below:

$R_{t+1}=0.9R_t+0.2C_t$

Also, 20% of city residents moved to the rural residents in the beginning of the year t+1.

Therefore, the number of city residents in the beginning of the year t+1 is as follows:

$C_{t+1}=0$