document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=882113>Question 882113</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Suppose the half-life of a certain radioactive isotope is 11 minutes.  If 21 per cent of the initial quantity is remaining, how many minutes old is the isotope?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:  t = ?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #532707 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=532707\">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=A=Ie%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"A=Ie%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Exponential Decay Equation.<BR>\n" );
document.write( "A = final amount<BR>\n" );
document.write( "I = initial amount<BR>\n" );
document.write( "t time in minutes<BR>\n" );
document.write( "k = constant for the specific decaying material\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You know these values:<BR>\n" );
document.write( "A=21<BR>\n" );
document.write( "I=100<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The 11 minutes half life information allows you to find k.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "USE HALF LIFE TO FIND k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%29=ln%28I%29%2B%28-kt%29ln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28A%29=ln%28I%29%2B%28-kt%29ln%28e%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%28I%29=-kt%2A1 ALIGN=MIDDLE  ALT=\"ln%28A%29-ln%28I%29=-kt%2A1\"   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%29-ln%28A%29 ALIGN=MIDDLE  ALT=\"kt=ln%28I%29-ln%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------you will use this again later.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28ln%28I%29-ln%28A%29%29%2Ft ALIGN=MIDDLE  ALT=\"k=%28ln%28I%29-ln%28A%29%29%2Ft\"   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%28k=%281%2Ft%29ln%28I%2FA%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=%281%2Ft%29ln%28I%2FA%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---as a formula.<BR>\n" );
document.write( "The half-life data meant I=1, A=1/2, t=11.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F11%29ln%281%2F%281%2F2%29%29=%281%2F11%29ln%282%29 ALIGN=MIDDLE  ALT=\"k=%281%2F11%29ln%281%2F%281%2F2%29%29=%281%2F11%29ln%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=0.06301 ALIGN=MIDDLE  ALT=\"k=0.06301\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "Decay Equation Model, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28A=Ie%5E%28-0.06301t%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28A=Ie%5E%28-0.06301t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "USE DECAY EQUATION TO ANSWER t.<BR>\n" );
document.write( "Start from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28I%29-ln%28A%29 ALIGN=MIDDLE  ALT=\"kt=ln%28I%29-ln%28A%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=%281%2Fk%29ln%28I%2FA%29%29 ALIGN=MIDDLE  ALT=\"highlight%28t=%281%2Fk%29ln%28I%2FA%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Substitute the known values for k, I, and A; and compute t.<BR>\n" );
document.write( "A=21, I=100, k=0.06301. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );