document.write( "Question 289917: 1) When a ball is dropped to the floor it bounces to 4/5th of the height from which it has been dropped. If it is dropped from a height of 2 meters, after how many bounces will its height go below ½ a meter?\r
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Algebra.Com's Answer #209881 by Fombitz(32388) $\"\"$ $\"About$

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n=0,First height, Zero bounces = $\"h%280%29=2\"$
\n" ); document.write( "n=1,Second height, 1 bounce = $\"h%281%29%284%2F5%292=8%2F5\"$
\n" ); document.write( "n=2,Third height, 2 bounces = $\"h%282%29=%284%2F5%29%288%2F5%29=%284%2F5%29%284%2F5%292=%284%2F5%29%5E2%2A2\"$
\n" ); document.write( "n=3,Fourth height, 3 bounces = $\"h%283%29=%284%2F5%29%5E3%2A2\"$
\n" ); document.write( "You are looking for heights less than 1/2.
\n" ); document.write( " $\"h%28n%29=%284%2F5%29%5En%2A2=1%2F2\"$
\n" ); document.write( " $\"%284%2F5%29%5En=1%2F4\"$
\n" ); document.write( "Take the log base (4/5) of each side,
\n" ); document.write( " $\"n=log%280.8%2C0.25%29=log%2810%2C0.25%29%2Flog%2810%2C0.8%29\"$
\n" ); document.write( " $\"n=6.2\"$
\n" ); document.write( "Take the next integer bounce, $\"n=7\"$
\n" ); document.write( "On the seventh bounce the height will be less than (1/2).
\n" ); document.write( " $\"h=%284%2F5%29%5E7%2A2=0.42\"$
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