SOLUTION: A ball is dropped vertically from a height of 50 meters. After each bounce, the ball reaches a maximum height equal to 80 percent of the maximum height of the previous bounce. a.)

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Question 867349: A ball is dropped vertically from a height of 50 meters. After each bounce, the ball reaches a maximum height equal to 80 percent of the maximum height of the previous bounce.
a.) Write the first three terms of the sequence. Explain how you know what they are.
b.) Find the height to the nearest tenth of a meter of the ball after the tenth bounce. Show and explain your work.''.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h%5Bn%5D+ be the maximum height of the
ball after the +n+th bounce
+h%5Bn%5D+=+50%2A.8%5En+
-----------------------
+h%5B1%5D+=+50%2A.8+
+h%5B1%5D+=+40+
--------------------
+h%5B2%5D+=+50%2A.8%5E2+
+h%5B2%5D+=+32+
------------------
+h%5B3%5D+=+50%2A.8%5E3+
+h%5B3%5D+=+25.6+
----------------------
Each result is +.8+ of the previous result
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+h%5B10%5D+=+50%2A.8%5E10+
+h%5B10%5D+=+50%2A.1074+
+h%5B10%5D+=+5.4+ m
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You could do successive multiplications
but I used a calculator