document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892641>Question 892641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A substance decays exponentially. If the 80 ounces of the substance decays to 9 ounces in 3 hours. What is the half - life of the substance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540673 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=540673\">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=p=Ie%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"p=Ie%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, generalized exponential decay equation<BR>\n" );
document.write( "p, how much present at time t starting from initial amount I<BR>\n" );
document.write( "I, initial amount when t=0<BR>\n" );
document.write( "t, time<BR>\n" );
document.write( "k, a constant<BR>\n" );
document.write( "e, the Euler number, base of Natural logarithm\r<BR>\n" );
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document.write( "First, find k using I=80, p=9, t=3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29=ln%28Ie%5E%28-kt%29%29 ALIGN=MIDDLE  ALT=\"ln%28p%29=ln%28Ie%5E%28-kt%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=ln%28I%29%2Bln%28e%5E%28-kt%29%29=ln%28p%29 ALIGN=MIDDLE  ALT=\"ln%28I%29%2Bln%28e%5E%28-kt%29%29=ln%28p%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%28I%29%2B%28-k%29t%2A1=ln%28p%29 ALIGN=MIDDLE  ALT=\"ln%28I%29%2B%28-k%29t%2A1=ln%28p%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%28p%29-ln%28I%29 ALIGN=MIDDLE  ALT=\"-kt=ln%28p%29-ln%28I%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=-%281%2Ft%29%28ln%28p%29-ln%28I%29%29 ALIGN=MIDDLE  ALT=\"k=-%281%2Ft%29%28ln%28p%29-ln%28I%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=highlight%28k=-%281%2Ft%29%28ln%28p%2FI%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-%281%2Ft%29%28ln%28p%2FI%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the value of k:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-%281%2F3%29%28ln%289%2F80%29%29 ALIGN=MIDDLE  ALT=\"k=-%281%2F3%29%28ln%289%2F80%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=highlight%28k=0.728%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.728%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using k as a positive value.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Half-Life<BR>\n" );
document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=I%2F2 ALIGN=MIDDLE  ALT=\"p=I%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=I%2F2=Ie%5E%28-0.728%2At%29 ALIGN=MIDDLE  ALT=\"p=I%2F2=Ie%5E%28-0.728%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=e%5E%28-0.728t%29 ALIGN=MIDDLE  ALT=\"1%2F2=e%5E%28-0.728t%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%281%2F2%29=-0.728t%2A1 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=-0.728t%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-1%2F%280.728%29ln%281%2F2%29 ALIGN=MIDDLE  ALT=\"t=-1%2F%280.728%29ln%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=highlight%28t=0.952%29 ALIGN=MIDDLE  ALT=\"highlight%28t=0.952%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in hours. </SPAN>\n" );
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