A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball.

The first drop makes the ball travel 16 m.

Then the maximum height decreases to 16 x 0.81

And the distance traveled is twice the distance traveled.

If we make a pattern, this forms a geometric progression in which the common ratio is 0.81 and the first term is 16.

The sum of this series: a / (1 - r)

= 16 (1 - 0.81)

= 84 feet

This is the upward height, and the ball returns every time so:

Total distance = 84 x 2

= 168 feet