Answer
135 feet
Work Step by Step
We know that the distance the ball travels is given by the following expression:
$$2\times \sum _{n=1}^{\infty }(15)(.8^n)$$
Note, we multiply by 2 since the ball bounces down and then goes up for each bounce. Simplifying:
$$ = 15(5-0.8^0)\times 2 \\ = 120 $$
Adding the initial 15 foot drop, the total is:
$$ =120+15 \\ =135 \ ft$$
