document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=577777>Question 577777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr. If 97.7% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? \r<BR>\n" );
document.write( "\n" );
document.write( "Please make this simple.  Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370381 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=370381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half-life of 234U, uranium-234, is 2.52 multiplied by 105 yr.<BR>\n" );
document.write( " If 97.7% of the uranium in the original sample is present,<BR>\n" );
document.write( " what length of time (to the nearest thousand years) has elapsed? <BR>\n" );
document.write( ":<BR>\n" );
document.write( "The radioactive decay formula: A = Ao*2^(-t/h) where:<BR>\n" );
document.write( "A = resulting amt after t time<BR>\n" );
document.write( "Ao = initial amt (t=0)<BR>\n" );
document.write( "h = half-life of substance<BR>\n" );
document.write( "t = time in yrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I think you mean the half-life of uranium-234 is: 2.52(10^5) yrs<BR>\n" );
document.write( "Let Ao = 1,<BR>\n" );
document.write( "A = .977<BR>\n" );
document.write( " find t<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1*2^[-t/2.52(10^5)] = .977<BR>\n" );
document.write( "using logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%5E%28-t%2F2.52%2810%5E5%29%29%29+=+Log%28.977%29 ALIGN=MIDDLE  ALT=\"log%282%5E%28-t%2F2.52%2810%5E5%29%29%29+=+Log%28.977%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "log equiv of exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F%282.52%2810%5E5%29%29 ALIGN=MIDDLE  ALT=\"-t%2F%282.52%2810%5E5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*log(2) = log(.977)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F%282.52%2810%5E5%29%29 ALIGN=MIDDLE  ALT=\"-t%2F%282.52%2810%5E5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.977%29%2Flog%282%29 ALIGN=MIDDLE  ALT=\"log%28.977%29%2Flog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using a calc <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F%282.52%2810%5E5%29%29 ALIGN=MIDDLE  ALT=\"-t%2F%282.52%2810%5E5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.033569<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.033569%2A-2.52%2810%5E5%29 ALIGN=MIDDLE  ALT=\"-.033569%2A-2.52%2810%5E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t = +8459.5 ~ 8000 yrs to the nearest thousand<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );