document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118991>Question 1118991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the table for the radioactive isotope. (Round your answer to two decimal places.) \r<BR>\n" );
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document.write( "isotope: RA^226<BR>\n" );
document.write( "Half Life (Years): 1599<BR>\n" );
document.write( "Initial Quantity: 10g<BR>\n" );
document.write( "Amount after 1000 years: UNKNOWN </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734438 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution by tutor @josgarithmetic, using logs, ends up with the right answer but seems like a very inefficient way to solve the problem.<br><BR>\n" );
document.write( "The solution by tutor @ikleyn is much simpler and also obtains the right answer.  But I note that scientists like to use exponentials with negative exponents to indicate decay, so her initial equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28t%29+=+M%2A%282%5E%28-n%29%29 ALIGN=MIDDLE  ALT=\"M%28t%29+=+M%2A%282%5E%28-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where n is the number of half lives.<br><BR>\n" );
document.write( "For me, it is much more natural to write the equation in a way that clearly shows the amount remaining becomes half as much after each half life:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%28t%29+=+M%2A%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"M%28t%29+=+M%2A%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So my path to the solution of the problem would be a single calculation:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%281%2F2%29%5E%281000%2F1599%29+=+6.48 ALIGN=MIDDLE  ALT=\"10%281%2F2%29%5E%281000%2F1599%29+=+6.48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use both methods as you practice other half life problems and see which works better for you. </SPAN>\n" );
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