Let's call the distance (in feet) that the ball travels between the -th and -th bounce.
What is ? ? ? in function of ? in function of ?
This is a classic geometric series.
Each is 70% of the previous.
Downward the ball travels 13+9.1+6.37+4.459+.........
Upward the ball travels 9.1+6.37+4.459+..............
We can assume the total distance the ball travels, S, can be found by adding the infinite series.
Now we can use the formula