document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378561>Question 378561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radioactive element americium-241 has half the life of 432 years. Suppose we start with a 45-g mass of americium-241, how much would be left after 343 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268892 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=268892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for determining the amount of substance left is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+Ce%5E%28kt%29 ALIGN=MIDDLE  ALT=\"A+=+Ce%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where C is the initial amount, k is the decay constant, and t is time. We must solve for k:\r<BR>\n" );
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document.write( "Given the half-life of 432 years, we may plug in t:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F2+=+Ce%5E%28432k%29 ALIGN=MIDDLE  ALT=\"C%2F2+=+Ce%5E%28432k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+=+e%5E%28432k%29 ALIGN=MIDDLE  ALT=\"1%2F2+=+e%5E%28432k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking ln of both sides,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%281%2F2%29+=+432k ALIGN=MIDDLE  ALT=\"ln+%281%2F2%29+=+432k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+%28ln+%281%2F2%29%29%2F432 ALIGN=MIDDLE  ALT=\"k+=+%28ln+%281%2F2%29%29%2F432\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -0.00160...\r<BR>\n" );
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document.write( "Now, we substitute t = 343 years to our equation to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+45%2Ae%5E%28343%2A-.00160%29 ALIGN=MIDDLE  ALT=\"A+=+45%2Ae%5E%28343%2A-.00160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 25.95376 (grams) </SPAN>\n" );
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