Question

A ball bounces back 0.6 of its height on every bounce. If a ball is dropped 200 feet, how high does it bounce the fifth bounce? Round to the nearest tenth.

Answer 1

It is asking you to slice off 40% of the bounce height in each subsequent bounce.

So you start with full height 1, that's n = 0 bounces. Then after n = 1 bounce the new height is .6. After the second bounce, n = 2, the height becomes .6 X .6 = .36. And after n = 3, we have .6 X .6 X .6 = .216

So by induction we see that h(n = 5) = .6^n = .6^5 = 0.07776 = .078 of its original height or H = .078*200 = 15.6 ft. after five bounces. ANS. 16.0 if rounded to the nearest tenth

:)