SOLUTION: A ball is dropped from 30 meters. It bounces to 88 % of its previous height on each bounce. How high will the ball bounce on its 5th bounce?

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Question 564302: A ball is dropped from 30 meters. It bounces to 88 % of its previous height on each bounce. How high will the ball bounce on its 5th bounce?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To analyze problem, let +h+ = the starting height
let +k+ = the fraction of the previous height that
is the next height
starting height: +h+
After 1st bounce, +k%2Ah+
After 2nd bounce, +k%2A%28k%2Ah%29+
After 3rd bounce, +k%2A%28k%2A%28k%2Ah%29%29+
After 4th bounce, +k%2A%28k%2A%28k%2A%28k%2Ah%29%29%29+
After 5th bounce, +k%2A%28k%2A%28k%2A%28k%2A%28k%2Ah%29%29%29%29+
-----------------------------------
This sequence is +h+, +k%2Ah+, +k%5E2%2Ah+,
+k%5E3%2Ah+, +k%5E4%2Ah+, +k%5E5%2Ah+
---------------
given:
+h+=+30+ m
+k+=+.88+
On it's 5th bounce, ball will reach heigh of
+.88%5E5+%2A+30+=+.5277%2A30+
+15.832+ m