Answer to Question #245142 in Algebra for ummi

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

$h_0=9$

$h_n=h_0(\frac{2}{3})^n=9(\frac{2}{3})^n$

$h_n=\frac{64}{81}\to 9(\frac{2}{3})^n=\frac{64}{81}\to (\frac{2}{3})^n=\frac{2^6}{3^6}$

Thus, n=6.

The ball bounced 6 times.