document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395072>Question 395072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The half life of thorium-229 is 7340 yrs. how long will it take a sampleof this substance to decay to 20% of its original amount?\r<BR>\n" );
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document.write( "That is the problem. I need help finding the solution. I know I will use the model A=Aoe^kt. I believe it would go something like:\r<BR>\n" );
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document.write( "A/2=Ao/2 ^kt<BR>\n" );
document.write( "0.2=???\r<BR>\n" );
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document.write( "I need to find my K before I can go further, but I am not sure how to do that. I would appreciate any help! Thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280423 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=280423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half life of thorium-229 is 7340 yrs. <BR>\n" );
document.write( "how long will it take a sampleof this substance to decay to 20% of its original amount? <BR>\n" );
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document.write( "I think the equation should be:<BR>\n" );
document.write( "A = Ao*2^(-t/h)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "A = amt after t yrs<BR>\n" );
document.write( "Ao = initial amt<BR>\n" );
document.write( "t = time in yrs<BR>\n" );
document.write( "h = half-life of the substance<BR>\n" );
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document.write( "Using the initial amt, Ao = 1, then A = .2<BR>\n" );
document.write( "2^(-t/7340) = .2<BR>\n" );
document.write( "Using natural logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F7340 ALIGN=MIDDLE  ALT=\"-t%2F7340\"   DISABLED_style= \"max-width:90%; height:auto;\" >*ln(2) = ln(.2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F7340 ALIGN=MIDDLE  ALT=\"-t%2F7340\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.2%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.2%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%2F7340 ALIGN=MIDDLE  ALT=\"-t%2F7340\"   DISABLED_style= \"max-width:90%; height:auto;\" >= -2.3219281<BR>\n" );
document.write( "t = -7340 * -2.3219281<BR>\n" );
document.write( "t = 17,043 yrs<BR>\n" );
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document.write( "Check solution on calc:<BR>\n" );
document.write( " enter 2^(-17043/7340), result: .19999 ~ .2, confirms our solution of t = 17,043 yrs </SPAN>\n" );
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