document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=711861>Question 711861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A radioactive isotope has a half-life of 1.2 billion years. As measured by the presence of the isotope and its stable decay product, a rock originally contained 10 grams of the radioactive isotope, and now contains 1.25 grams. Approximately how many years old is the rock?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437671 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=437671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Decay relationship is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5De%5E%28kt%29 ALIGN=MIDDLE  ALT=\"A=A%5B0%5De%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is billions of years.\r<BR>\n" );
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document.write( "FIND THE CONSTANT, k<BR>\n" );
document.write( "half life is 1.2 billion years.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1%2F2 ALIGN=MIDDLE  ALT=\"A=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D=1 ALIGN=MIDDLE  ALT=\"A%5B0%5D=1\"   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=1%2Ae%5E%28k%2A1.2%29 ALIGN=MIDDLE  ALT=\"1%2F2=1%2Ae%5E%28k%2A1.2%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=ln%28e%5E%28k1.2%29%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=ln%28e%5E%28k1.2%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%281%2F2%29=1.2k%2A1 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=1.2k%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28ln%281%2F2%29%29%2F1.2 ALIGN=MIDDLE  ALT=\"k=%28ln%281%2F2%29%29%2F1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-.578 ALIGN=MIDDLE  ALT=\"k=-.578\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "HOW MUCH TIME PASSED or HOW OLD IS THE SAMPLE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=A%5B0%5De%5E%28-0.578t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=A%5B0%5De%5E%28-0.578t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Best to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then substitute values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29=ln%28A%5B0%5D%2Ae%5E%28-0.578t%29%29 ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28A%5B0%5D%2Ae%5E%28-0.578t%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%28A%29=ln%28A%5B0%5D%29%2Bln%28e%5E%28-.578t%29%29 ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28A%5B0%5D%29%2Bln%28e%5E%28-.578t%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%28A%29=ln%28A%5B0%5D%29%2B-0.578%2At%2A1 ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28A%5B0%5D%29%2B-0.578%2At%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29-ln%28A%5B0%5D%29=-0.578%2At ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28A%5B0%5D%29=-0.578%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%28A%29-ln%28A%5B0%5D%29%29%2F%28-0.578%29 ALIGN=MIDDLE  ALT=\"t=%28ln%28A%29-ln%28A%5B0%5D%29%29%2F%28-0.578%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=%28ln%28A%5B0%5D%29-ln%28A%29%29%2F%280.578%29%29 ALIGN=MIDDLE  ALT=\"highlight%28t=%28ln%28A%5B0%5D%29-ln%28A%29%29%2F%280.578%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now substitute the given values to compute t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=%28ln%2810%29-ln%281.25%29%29%2F0.578%29 ALIGN=MIDDLE  ALT=\"highlight%28t=%28ln%2810%29-ln%281.25%29%29%2F0.578%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, billion years<BR>\n" );
document.write( " </SPAN>\n" );
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