document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143472>Question 1143472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An unknown radioactive element decays into non-radioactive substances. In <BR>\n" );
document.write( "700 days the radioactivity of a sample decreases by 29 percent. \r<BR>\n" );
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document.write( "(a) What is the half-life of the element? <BR>\n" );
document.write( "half-life:  <BR>\n" );
document.write( "    (days) \r<BR>\n" );
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document.write( "(b) How long will it take for a sample of <BR>\n" );
document.write( "100mg to decay to 54mg? <BR>\n" );
document.write( "time needed: <BR>\n" );
document.write( "             (days)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764300 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=764300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The radioactivity does not decrease.  What you mean is the amount of radioactive material decreases by 29%.<br><BR>\n" );
document.write( "(a) calculating the half life....<br><BR>\n" );
document.write( "(1) Determine the number of half lives required for the amount of radioactive material to decrease by 29% -- i.e., to decay to 71% of the original amount.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5En+=+0.71 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5En+=+0.71\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28%281%2F2%29%29+=+log%28%280.71%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28%281%2F2%29%29+=+log%28%280.71%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%28%280.71%29%29%2Flog%28%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%280.71%29%29%2Flog%28%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.4941 to 4 decimal places<br><BR>\n" );
document.write( "(2) Determine the half life, given that 700 days is 0.4941 half lives.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=half+life+=+700%2F0.4941 ALIGN=MIDDLE  ALT=\"half+life+=+700%2F0.4941\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1416.69 days to 2 decimal places.<br><BR>\n" );
document.write( "(a) ANSWER: the half life is 1416.69 days<br><BR>\n" );
document.write( "(b) Determining the number of days for a sample of 100mg to decay to 54mg....<br><BR>\n" );
document.write( "(1) Determine the number of half lives.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5En+=+0.54%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5En+=+0.54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28%281%2F2%29%29+=+log%28%280.54%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28%281%2F2%29%29+=+log%28%280.54%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%28%280.54%29%29%2Flog%28%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%280.54%29%29%2Flog%28%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.889 to 3 decimal places<br><BR>\n" );
document.write( "(2) Determine the number of days in 0.889 half lives.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.889%2A1416.69 ALIGN=MIDDLE  ALT=\"0.889%2A1416.69\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1259 to the nearest whole number<br><BR>\n" );
document.write( "(b) ANSWER: about 1259 days for 100mg to decay to 54mg. </SPAN>\n" );
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