document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=37108>Question 37108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A computer is infected with the Boro virus.  Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc.  How long until 100 million computers are infected </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22809 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=22809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "Let's call X to the number of 5-minute blocks that have passed since the first computer was infected.\r<BR>\n" );
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document.write( "When X = 1 (5 minutes have passed), there are 20 infected computers<BR>\n" );
document.write( "When X = 2 (10 minutes have passed), there are 20*20 = 20^2 infected computers<BR>\n" );
document.write( "When X = 3 (15 minutes have passed), there are 20*20*20 = 20^3 infected computers<BR>\n" );
document.write( "and so on...\r<BR>\n" );
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document.write( "So the formula for the number of infected computers is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+20%5EX ALIGN=MIDDLE  ALT=\"Y+=+20%5EX\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We want to find X such that Y is equal to 100,000,000:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100000000+=+20%5EX ALIGN=MIDDLE  ALT=\"100000000+=+20%5EX\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Applying natural logarithm:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28100000000%29+=+X%2Aln%2820%29 ALIGN=MIDDLE  ALT=\"ln%28100000000%29+=+X%2Aln%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=ln%28100000000%29%2Fln%2820%29+=+6.1489 ALIGN=MIDDLE  ALT=\"X=ln%28100000000%29%2Fln%2820%29+=+6.1489\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, there will be 100,000,000 infected computers after 6.1489 5-minute blocks, or 6.1489*5 = 30.74 minutes\r<BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!<BR>\n" );
document.write( " </SPAN>\n" );
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