document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=832377>Question 832377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The amount of grams \"A\" of a certain radioactive substance dumped in the Craney Island Disposal Area at time \"t\" is given by the formula  \"A=(Ao)e^(-0.1t)\"<BR>\n" );
document.write( "where \"t\" is the time measured in days and \"Ao\" is the original amount of material. Find the half-life of this substance.\r<BR>\n" );
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document.write( "Would really appreciate any help with this. I have tried everything I could think of but because there are no amounts to work with I'm not sure what to do with it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502021 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=502021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The amount of grams \"A\" of a certain radioactive substance dumped in the Craney Island Disposal Area at time \"t\" is given by the formula \"A=(Ao)e^(-0.1t)\"<BR>\n" );
document.write( "where \"t\" is the time measured in days and \"Ao\" is the original amount of material. Find the half-life of this substance. <BR>\n" );
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document.write( "A(t) = Ao*e^(-0.1t)<BR>\n" );
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document.write( "Ao is the amount you start with.<BR>\n" );
document.write( "A(t) is the amount after time = t.<BR>\n" );
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document.write( "If A(t) is (1/2)Ao, e^(-0.1t) must be 1/2<BR>\n" );
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document.write( "Solve: e^(-0.1t) = 1/2<BR>\n" );
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document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "-0.1t = ln(0.5) = -0.6931<BR>\n" );
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document.write( "t = -0.6931/-0.1 = 6.93 days.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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