Chapter 9, Problem 40RE

(A)

To determine

To calculate:The matrices $S_1,S_2,S_3,$ and round the entries to two decimal places for the matrix $S_0=\left[\begin{array}{cc}.14& .86\end{array}\right]$ and the given transition matrix $P$.

$\begin{array}{l}\text{ Five years later}\\ II\\ \begin{array}{c}\begin{array}{l}\text{Current}\\ \text{year}\end{array}\end{array}\begin{array}{c}I\\ I^{\prime }\end{array}\left[\begin{array}{cc}.95& .05\\ .40& .60\end{array}\right]=P\end{array}$

Where, $I$ represents the population of Internet users.

(B)

To determine

The new table which compares the result from part (A) with the data given in Table 1, which represents the percentage of U.S. population of Internet users.

$\begin{array}{l}\text{Table 1}\\ \begin{array}{cc}\text{Year}& \text{Percent}\\ 1995& 14\\ 2000& 49\\ 2005& 68\\ 2010& 79\end{array}\end{array}$

( C )

To determine

The percentage of the adult U.S. population of Internet users in the long-run for the given transition matrix.