document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946030>Question 946030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Radium-221 has a half-life of 30 sec. How long will it take for 91% of a sample to decay? (Round your answer to the nearest whole number.)<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 #577104 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=577104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Material has half life of t seconds.  How long will it take for s percent of Material sample to decay?\r<BR>\n" );
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document.write( "Question is to find how much time until quantity present changes from I to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28100-s%29%2F100%29%2AI ALIGN=MIDDLE  ALT=\"%28%28100-s%29%2F100%29%2AI\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "First find k, and then use k to find time to let s percent of sample to decay.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=I%2Ae%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"y=I%2Ae%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ie%5E%28-kt%29=y ALIGN=MIDDLE  ALT=\"Ie%5E%28-kt%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ae%5E%28-kt%29=%281%2F2%29 ALIGN=MIDDLE  ALT=\"1%2Ae%5E%28-kt%29=%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28-kt%29%29=-ln%282%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28-kt%29%29=-ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-kt=-ln%282%29 ALIGN=MIDDLE  ALT=\"-kt=-ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282%29%2Ft ALIGN=MIDDLE  ALT=\"k=ln%282%29%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you know t=30 seconds and want the value...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282%29%2F30 ALIGN=MIDDLE  ALT=\"k=ln%282%29%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.0231%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.0231%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Model Revised:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=I%2Ae%5E%28-0.0231t%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=I%2Ae%5E%28-0.0231t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Starting with I=1, t is what when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-s%2F100 ALIGN=MIDDLE  ALT=\"y=1-s%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "(Your value given for s is 91).<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28-0.0231t%29%29=ln%281-s%2F100%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28-0.0231t%29%29=ln%281-s%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.0231t=ln%281-s%2F100%29 ALIGN=MIDDLE  ALT=\"-0.0231t=ln%281-s%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t=-ln(1-s/100)/(-0.0231)<BR>\n" );
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document.write( "Easier to avoid sign mistakes if directly using the actual values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28-0.0231t%29%29=ln%28%28100-91%29%2F100%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28-0.0231t%29%29=ln%28%28100-91%29%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.0231t=ln%289%2F100%29 ALIGN=MIDDLE  ALT=\"-0.0231t=ln%289%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0231t=ln%28100%2F9%29 ALIGN=MIDDLE  ALT=\"0.0231t=ln%28100%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=ln%28100%2F9%29%2F%280.0231%29 ALIGN=MIDDLE  ALT=\"t=ln%28100%2F9%29%2F%280.0231%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=104%29 ALIGN=MIDDLE  ALT=\"highlight%28t=104%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, seconds. </SPAN>\n" );
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