document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168807>Question 168807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cell Division:  One leukemic cell injected into a healthy mouse will divide into two cells in about 1/2 day.  At the end of the day these two cells will divide again, with the doubling process continuing each 1/2 until there are 1 billion cells, at which time the mouse dies.  On which day after the experiment is started does this happen?\r<BR>\n" );
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document.write( "I'm having a horrible time coming up with a formula for this problem.\r<BR>\n" );
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document.write( "I would appreciate any help you can give me on this one.  \r<BR>\n" );
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document.write( "Thank you so much, ahead of time!<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 #124458 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cell Division: One leukemic cell injected into a healthy mouse will divide into two cells in about 1/2 day. At the end of the day these two cells will divide again, with the doubling process continuing each 1/2 until there are2^x 1 billion cells, at which time the mouse dies. On which day after the experiment is started does this happen? <BR>\n" );
document.write( "I'm having a horrible time coming up with a formula for this problem. <BR>\n" );
document.write( "I would appreciate any help you can give me on this one. <BR>\n" );
document.write( "Thank you so much, ahead of time!<BR>\n" );
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document.write( "The divisions double the number of cells, so the number will be a power of 2, as in 2, 4, 8, 16, 32 etc.<BR>\n" );
document.write( "The power of 2 closest to \"about a billion\" is 2^30 = 1,073,741,824.  BTW, this is also a Giga, as in a Gigabyte of RAM, or space on a hard drive.<BR>\n" );
document.write( "Anyway, it will take 30 divisions, so that's 30 half-days, or 15 days.<BR>\n" );
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document.write( "If you don't happen to know that 2^30 is apx a billion (some people don't):<BR>\n" );
document.write( "2^x = 1,000,000,000<BR>\n" );
document.write( "x*log(2) = log(1000000000)<BR>\n" );
document.write( "x*0.30103 = 9<BR>\n" );
document.write( "x = 29.9 half days\r<BR>\n" );
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