document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703263>Question 703263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this word problem, I'm out of my depth:<BR>\n" );
document.write( "If 12 g of a radioactive substance are present initially and 4 yr later only 6 g remain, how much of the substance will be present after 7 yr?\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Samara  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433421 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=433421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Radioactive decay may work like an exponential decay.<BR>\n" );
document.write( "Using t for years, A[0] for starting amount, A[t] for amount at time t,<BR>\n" );
document.write( "We may use formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D=A%5B0%5De%5E%28k%2At%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=A%5B0%5De%5E%28k%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's not clear if you mean first 4 years and then 3 more years, or are you just saying, \"half life is 4 years\"+\".  After 7 years.\"\r<BR>\n" );
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document.write( "Starting with half life, we want to find k.<BR>\n" );
document.write( "In a 4 year period, t=4, and A quantity will be reduced to (1/2)*A.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29=1%2Ae%5E%28k%2A4%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29=1%2Ae%5E%28k%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=ln%28e%5E%28k%2A4%29%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=ln%28e%5E%28k%2A4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=k%2A4 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=k%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28ln%281%2F2%29%29%2F4 ALIGN=MIDDLE  ALT=\"k=%28ln%281%2F2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Computing k gives us k = 0.173.<BR>\n" );
document.write( "Our decay formula then is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D=A%5B0%5D%2Ae%5E%28-0.173%2At%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=A%5B0%5D%2Ae%5E%28-0.173%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW, if you want the quantity remaining after 7 years and the starting quantity is 12 grams, then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B7%5D=12%2Ae%5E%28-0.173%2A7%29 ALIGN=MIDDLE  ALT=\"A%5B7%5D=12%2Ae%5E%28-0.173%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B7%5D=12%2A0.2979 ALIGN=MIDDLE  ALT=\"A%5B7%5D=12%2A0.2979\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A[7]=3.6 grams<BR>\n" );
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