document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380265>Question 380265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have this chart that talks about the half life of these and they are all different. I am not really understanding what the concept is here. How do I even attempt to answer this question...I don't even understand. I looked up half-life and it just doesn't make sense. Please explain and help me solve this problem.\r<BR>\n" );
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document.write( "The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years?\r<BR>\n" );
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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 #269871 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=269871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"I have this chart that talks about the half life of these and they are all different. I am not really understanding what the concept is here. How do I even attempt to answer this question...I don't even understand. I looked up half-life and it just doesn't make sense. Please explain and help me solve this problem. <BR>\n" );
document.write( "The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years? <BR>\n" );
document.write( "_____?\"\r<BR>\n" );
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document.write( "Half-life is how long it takes for a particular element, in this case Radium-226 to decrease by half. If there is just one radioactive atom you will not end up with half an atom, there will be either 0 atoms left or one atom left.  Different elements decay at different rates.\r<BR>\n" );
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document.write( "N sub t = quantity still remaining after time t<BR>\n" );
document.write( "N sub 0 = initial quantity<BR>\n" );
document.write( "t sub 1/2 = half-life of decaying element<BR>\n" );
document.write( "N sub t = N sub 0 * (1/2)^(t / t sub 1/2)\r<BR>\n" );
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document.write( "N sub 0 = 100 mg<BR>\n" );
document.write( "t sub 1/2 = 1590 years\r<BR>\n" );
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document.write( "let N sub t = 50 mg<BR>\n" );
document.write( "50 = 100 * (1/2)^(t/1590)<BR>\n" );
document.write( "50/100 = (1/2)^(t/1590)<BR>\n" );
document.write( "1/2 = (1/2)^(t/1590)<BR>\n" );
document.write( "t must be 1590 years\r<BR>\n" );
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document.write( "now for 3000 years:<BR>\n" );
document.write( "N sub 0 = 100 mg<BR>\n" );
document.write( "N sub t = ?<BR>\n" );
document.write( "t = 3000 years<BR>\n" );
document.write( "t sub 1/2 = 1590 years<BR>\n" );
document.write( "N sub t = 100 * (1/2)^(3000/1590)<BR>\n" );
document.write( "N sub t = 27.040759 mg to 6 places<BR>\n" );
document.write( "N sub t = 27.041 mg to 3 places\r<BR>\n" );
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document.write( " </SPAN>\n" );
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