Final answer:
The total distance traveled by the ball is 23.75 feet.
Step-by-step explanation:
In this problem, the ball drops from a height of 19 feet and each time it hits the ground, it bounces up 20% of the height it falls. This forms a geometric series with a common ratio of 0.2. The total distance traveled by the ball can be found by summing an infinite geometric series.
The sum of an infinite geometric series is given by the formula: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.
In this case, the first term is 19 feet and the common ratio is 0.2. Plugging these values into the formula, we get: S = 19 / (1 - 0.2) = 23.75 feet.
Therefore, the total distance traveled by the ball is 23.75 feet.