document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130481>Question 1130481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Last one tonight and I believe this will help complete my study guide for this chapter.  Thank you in advance.\r<BR>\n" );
document.write( "\n" );
document.write( "The decay rate of a certain chemical is 9.5&#8203;% per year. What is its &#8203;half-life?  Use the exponential decay model &#8203;P(t)=P0e Superscript -kt)<BR>\n" );
document.write( "&#8722;kt where k is the decay&#8203; rate, and P0 is the original amount of chemical.<BR>\n" );
document.write( "The&#8203; half-life of the chemical is ___years.<BR>\n" );
document.write( "&#8203;(Round to the nearest&#8203; integer.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747151 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=747151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Model is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=P%5Bo%5De%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"P%28t%29=P%5Bo%5De%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and half life is value of t when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=%281%2F2%29%28P%5Bo%5D%29 ALIGN=MIDDLE  ALT=\"P%28t%29=%281%2F2%29%28P%5Bo%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "FIND k, first.<BR>\n" );
document.write( "Some variables changes just for notational and keyboard conveniences.\r<BR>\n" );
document.write( "\n" );
document.write( "y=p*e^(-kt)  instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29 ALIGN=MIDDLE  ALT=\"P%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bo%5D ALIGN=MIDDLE  ALT=\"P%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Ae%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"y=1%2Ae%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.095=1%2Ae%5E%28-k%2A1%29 ALIGN=MIDDLE  ALT=\"1-0.095=1%2Ae%5E%28-k%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  one year of decay time\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.905=e%5E%28-k%29 ALIGN=MIDDLE  ALT=\"0.905=e%5E%28-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.905%29=ln%28e%5E%28-k%29%29 ALIGN=MIDDLE  ALT=\"ln%280.905%29=ln%28e%5E%28-k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k=ln%280.905%29 ALIGN=MIDDLE  ALT=\"-k=ln%280.905%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-k=-0.099820 ALIGN=MIDDLE  ALT=\"-k=-0.099820\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0.099820 ALIGN=MIDDLE  ALT=\"k=0.099820\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Model can be stated  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P%28t%29=P%5Bo%5De%5E%28-0.09982t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28P%28t%29=P%5Bo%5De%5E%28-0.09982t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "FIND HALF-LIFE\r<BR>\n" );
document.write( "\n" );
document.write( "Using model as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=1%2Ae%5E%28-0.09982t%29 ALIGN=MIDDLE  ALT=\"1%2F2=1%2Ae%5E%28-0.09982t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take natural logs of both sides, simplify, and solve for t.\r<BR>\n" );
document.write( "\n" );
document.write( "result should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%2F2%5D=ln%282%29%2F0.09982 ALIGN=MIDDLE  ALT=\"t%5B1%2F2%5D=ln%282%29%2F0.09982\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );