document.write( "Question 1202082: A leak in the roof allows two drops through the first day, four drops through the second day, eight drops the third. At this rate, when will the 500th drop fall through? Show your work. \n" ); document.write( "

Algebra.Com's Answer #836717 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "A leak in the roof allows two drops through the first day, four drops through the second day, eight drops the third.
\n" ); document.write( "At this rate, when will the 500th drop fall through? Show your work.
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\n" ); document.write( "\n" ); document.write( "Anybody can solve this easy problem by making a Table similar to that below.\r
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document.write( " day		drops		total       total\r\n" );
document.write( "		this day	drops      drops+2\r\n" );
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document.write( "  1		  2		  2           4\r\n" );
document.write( "  2		  4		  6           8\r\n" );
document.write( "  3		  8		 14          16\r\n" );
document.write( "  4		 16		 30          32\r\n" );
document.write( "  5		 32		 62          64\r\n" );
document.write( "  6		 64		126         128\r\n" );
document.write( "  7		128		254         256\r\n" );
document.write( "  8		256		510         512\r\n" );
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document.write( "From the table, one can see that the 500th drop will fall on the 8th day.\r\n" );
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document.write( "If you want to create a theory around it, then add and consider\r\n" );
document.write( "an additional column (the last column in the table) by adding 2\r\n" );
document.write( "to the numbers in the 3rd column.  All these numbers are \r\n" );
document.write( "of the form  ,  where \"n\" is a sequential number of the day.\r\n" );
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document.write( "Then you can conclude that 500th drop will fall when n+1 = 9  (  = 512 ),  or n = 8.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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