document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136372>Question 1136372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An unknown radioactive element decays into non-radioactive substances. In 560 days the radioactivity of a sample decreases by 51 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 100 mg to decay to 47 mg? <BR>\n" );
document.write( "time needed: <BR>\n" );
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document.write( "The fraction of the material remaining after n half-lives is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5%29%5E%28n%29 ALIGN=MIDDLE  ALT=\"%28.5%29%5E%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(a) Determine the half-life<br><BR>\n" );
document.write( "In this problem, the amount of material decreased by 51% in 560 days; that means after 560 days 49% remains.  Use the basic formula to determine how many half-lives that is.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5%29%5En+=+0.49 ALIGN=MIDDLE  ALT=\"%28.5%29%5En+=+0.49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "n = 1.0291463  (to several decimal places, using a graphing calculator)<br><BR>\n" );
document.write( "So the half-life of the material is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560%2F1.0291463+=+544.14 ALIGN=MIDDLE  ALT=\"560%2F1.0291463+=+544.14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(b) Determine how long it will take a 100mg sample to decay to 47mg<br><BR>\n" );
document.write( "Use the basic formula to determine the number of half-lives it takes for the material to decay to where 47% remains, then multiply the half-life by that number.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5%29%5En+=+0.47 ALIGN=MIDDLE  ALT=\"%28.5%29%5En+=+0.47\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+1.0892673 ALIGN=MIDDLE  ALT=\"n+=+1.0892673\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0892673%2A544.14+=+592.7139 ALIGN=MIDDLE  ALT=\"1.0892673%2A544.14+=+592.7139\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It takes about 593 days for a 100mg sample to decay to 47mg. </SPAN>\n" );
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