document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073879>Question 1073879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a super-bouncy ball rebounds half the height it drops. the ball is dropped from a height of 176 feet. How far off the ground is the ball when it has travled a total of 500 feet?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688661 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The falls form a geometric series with initial term of 176 and a common ratio of (1/2)<BR>\n" );
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document.write( "The general form for the sum of a geometric series is<BR>\n" );
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document.write( "S(n) = a1 * (1-r^n) / (1-r)<BR>\n" );
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document.write( "For the falls, a(1) = 176 and r = (1/2)<BR>\n" );
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document.write( "S(n) = 176 * (1 - (1/2)^n) / (1 - (1/2))<BR>\n" );
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document.write( "For the rebounds, a(1) = 88 and r = (1/2)<BR>\n" );
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document.write( "S(n) = 88 * (1 - (1/2)^n) / (1 - (1/2))<BR>\n" );
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document.write( "We know<BR>\n" );
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document.write( "500 = (352 * (1 - (1/2)^(n+1))) + (176 * (1 - (1/2)^n))<BR>\n" );
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document.write( "divide both sides of = by 4<BR>\n" );
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document.write( "125 = (88 * (1 - (1/2)^(n+1))) + (44 * (1 - (1/2)^n))<BR>\n" );
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document.write( "125 = (88 * (1 - 2^(-n - 1))) + (44 * (1 - 2^(-n)))<BR>\n" );
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document.write( "7 * 2^n = 132<BR>\n" );
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document.write( "use definition of logarithm<BR>\n" );
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document.write( "n = 4.237<BR>\n" );
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document.write( "We calculate the rebounds for n = 4 and n = 3<BR>\n" );
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document.write( "S(4) = 88 * (1 - (1/2)^4) / (1 - (1/2)) = 165<BR>\n" );
document.write( "S(3) = 88 * (1 - (1/2)^(4.237)) / (1 - (1/2)) = 154<BR>\n" );
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document.write( "The ball is 165 - 154 = 11 feet above the ground<BR>\n" );
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