document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=753000>Question 753000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Under the onslaught of the college algebra second period class, a pile of homework problems decreased exponentially. It decreased form 900 to 500 problems in only 40 minutes. How long would it take until only 300 problems remained? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458170 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=458170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Under the onslaught of the college algebra second period class, a pile of homework problems decreased exponentially. It decreased form 900 to 500 problems in only 40 minutes. How long would it take until only 300 problems remained?<BR>\n" );
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document.write( "y = ab^x<BR>\n" );
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document.write( "You have 2 points (0,900) and (40,500)<BR>\n" );
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document.write( "Using (0,900) 900 = ab^0<BR>\n" );
document.write( "900 = a<BR>\n" );
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document.write( "y = 900*b^x<BR>\n" );
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document.write( "Using (40,500) solve for \"b\":<BR>\n" );
document.write( "500 = 900*b^40<BR>\n" );
document.write( "b^40 = 5/9<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "f(x) = 900(5/9)^(x/40)<BR>\n" );
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document.write( "How long would it take until only 300 problems remained?<BR>\n" );
document.write( "Solve: 300 = 900(5/9)^(x/40)<BR>\n" );
document.write( "(5/9)^(x/40) = 1/3<BR>\n" );
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document.write( "(x/40) = log(1/3)/log(5/9)<BR>\n" );
document.write( "x/40 = 1.87<BR>\n" );
document.write( "x = 75 minutes<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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