When a rubber ball is dropped on a particular surface , It bounces back to 8/10 of drop height. The ball's height after bounce x is * (8/10) ^ x times its drop height . What fraction of its drop height will the ball bounce up to after its fourth bounce ? Show your work

The fraction of its drop height after the fourth bounce is

Step-by-step explanation:

Let's suppose the rubber ball is dropped from a height H0. Every time the ball bounces back it reaches 8/10 of the initial drop height.

The ball's height H(x) after bounce number x is:

Simplifying:

After the fourth bounce, the height is:

The fraction of its drop height after the fourth bounce is