Chapter 8.1, Problem 19E

Woman in the Labor Force Referring to Example 5, consider a typical group of French women, of whom 47% currently work outside of the home. Assume that the same percentage of daughters follow in their mothers’ footsteps as with the American women-that is, that given by the matrix

$A=\left[\begin{array}{cc}.8& .3\\ .2& .7\end{array}\right].$

Use A and $A^2$ to determine the proportion of French women who work outside of the home in the next two generations. (Round to the nearest whole percent.)