A golf ball is manufactured so that if it is dropped from \( A \) feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce. 

\( a \) . Find an exponential equation that gives the height \( h \) the ball will attain during the \( n \) th bounce. 

\( h = a ^ { \star } ( 1 / 2 ) ^ { \wedge } ( n - 1 ) \) \( b \) . If the ball is dropped from \( 23 \) feet above the ground onto hard a surface, how high will it bounce on the \( 9 \) th bounce? On the \( 9 \) th bounce, the ball will reach a height of \( 23 / 512 \) feet. Preview