document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997699>Question 997699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tricky exponential decay word problem:\r<BR>\n" );
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document.write( "Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released into the air in a laboratory. If the resulting radiation level is 10% above the safe level, how long should the laboratory remain vacated? (Hint: To start with, determine what fraction of the \"resulting radiation level\" is the maximum safe level.) \r<BR>\n" );
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document.write( "The laboratory should remain vacated for ____days\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615675 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=615675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=Ie%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"y=Ie%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find k using the given half-life.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29=ln%28I%29-kt ALIGN=MIDDLE  ALT=\"ln%28y%29=ln%28I%29-kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29-ln%28I%29=-kt ALIGN=MIDDLE  ALT=\"ln%28y%29-ln%28I%29=-kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28I%29-ln%28y%29=kt ALIGN=MIDDLE  ALT=\"ln%28I%29-ln%28y%29=kt\"   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%28I%2Fy%29 ALIGN=MIDDLE  ALT=\"kt=ln%28I%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----will be re-used later<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2Ft%29ln%28I%2Fy%29 ALIGN=MIDDLE  ALT=\"k=%281%2Ft%29ln%28I%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute half life information data.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F3.8%29ln%281%2F%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"k=%281%2F3.8%29ln%281%2F%281%2F2%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=k=ln%282%29%2F3.8 ALIGN=MIDDLE  ALT=\"k=ln%282%29%2F3.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0.1824 ALIGN=MIDDLE  ALT=\"k=0.1824\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Refined Model, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=Ie%5E%28-0.1824t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=Ie%5E%28-0.1824t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The maximum safety level would be some 100%, not sure based on what units.  Ten percent above the safety level would be some  110% of these units for radon gas.  You want to calculate the time to decay from 110%  to 100%.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28I=110%2C+y=100%29 ALIGN=MIDDLE  ALT=\"system%28I=110%2C+y=100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Look back at the derivation made earlier, and starting from the step,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28I%2Fy%29 ALIGN=MIDDLE  ALT=\"kt=ln%28I%2Fy%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_green%28t=ln%28I%2Fy%29%2Fk%29 ALIGN=MIDDLE  ALT=\"highlight_green%28t=ln%28I%2Fy%29%2Fk%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%28110%2F100%29%2F%280.1824%29 ALIGN=MIDDLE  ALT=\"t=ln%28110%2F100%29%2F%280.1824%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%2811%2F10%29%2F%280.1824%29 ALIGN=MIDDLE  ALT=\"t=ln%2811%2F10%29%2F%280.1824%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=0.5225%2Adays%29 ALIGN=MIDDLE  ALT=\"highlight%28t=0.5225%2Adays%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------near enough to say 13 hours. </SPAN>\n" );
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