Chapter 2, Problem 9RP

Explanation of Solution

Expressing the given vectors using matrix multiplication:

Suppose $C_t$ be the number of children in Indiana at the beginning of the year $t$ and $A_t$ be the number of adults in Indiana at the beginning of year $t$.

Since during any year $t$, 5% of all the children become adults and 1% of all children die, the number of children at the beginning of the year  $t+1$ is 96% of the previous year.

Hence, the number of children in the beginning of the year  $t+1$ is,

$C_{t+1}=0.96C_t$

Also, during any year $t$ , 3% of all adults die. So, 97% of all adults will live in the beginning of the year $t+1$  .

Therefore, the number of adults in the beginning of the year   $t+1$ is,

$A_{t+1}=0$