document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433433>Question 433433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of a radioactive substance decayed to 91% of its original amount after a year. (Round your answers to two decimal places.) <BR>\n" );
document.write( "(a) What is the half-life of the substance?<BR>\n" );
document.write( "(b) How long would it take the sample to decay to 30% of its original amount?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300490 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of a radioactive substance decayed to 91% of its original amount after a year.<BR>\n" );
document.write( " (Round your answers to two decimal places.)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The decay formula: A = Ao*2^(-t/h)<BR>\n" );
document.write( "Where<BR>\n" );
document.write( "A = resulting amt after t time<BR>\n" );
document.write( "Ao = initial amt<BR>\n" );
document.write( "h = half-life the of substance<BR>\n" );
document.write( "t = time (yrs)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(a) What is the half-life of the substance?<BR>\n" );
document.write( "Let initial amt = 1<BR>\n" );
document.write( "1*2(-1/h) = .91<BR>\n" );
document.write( "Using nat logs<BR>\n" );
document.write( "ln(2^(-1/h)) = ln(.91)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fh ALIGN=MIDDLE  ALT=\"-1%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >*ln(2) = ln(.91)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fh ALIGN=MIDDLE  ALT=\"-1%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.91%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.91%29%2Fln%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=-1%2Fh ALIGN=MIDDLE  ALT=\"-1%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.13606<BR>\n" );
document.write( "h = -1/.13606 <BR>\n" );
document.write( "h = 7.35 yrs is the half-life<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(b) How long would it take the sample to decay to 30% of its original amount?<BR>\n" );
document.write( "1*2^(-t/7.35) = .3<BR>\n" );
document.write( "Doing it the same way with nat logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F7.35 ALIGN=MIDDLE  ALT=\"-t%2F7.35\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.3%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.3%29%2Fln%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=-t%2F7.35 ALIGN=MIDDLE  ALT=\"-t%2F7.35\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.737<BR>\n" );
document.write( "t = -7.35 * -1.737<BR>\n" );
document.write( "t = +12.77 yrs for 30% to remain </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );