Answer to Question #245031 in Algebra for mai

Question

A certain ball always rebounds 2/3 of the distance from which it falls. If the ball is

dropped from a height of 9 feet, and later it is observed rebounding to a height of 64/81 feet, then how many times did it bounce?

Answer 1

The height of the rebounding can be described as the next geometric sequence: $b(n)=9*({\frac 2 3})^{n}$ , where n-number of bouncies

We have next equation:

${\frac {64} {81}}=9*({\frac 2 3})^{x}$

$({\frac 2 3})^{x} = {\frac {64} {729}}$

$x=6$

The ball did bounce 6 times