document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836622>Question 836622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The half life of a radioactive substance is 2 hours. <BR>\n" );
document.write( "(a)What percentage of an initial sample will remain after 1 hour?<BR>\n" );
document.write( "(b)What percentage of an initial sample will remain after 7 hours?\r<BR>\n" );
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document.write( "I know the half life is the time it takes for a substance to disintegrate but I cant seem to solve the problem. Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504293 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=504293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half life is the amount of time for half of the substance to disintegrate.\r<BR>\n" );
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document.write( "Since the sample decays exponentially, the amount A(t) of the substance as a function of time t (in hours) is given by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A(t) = A_0 e^{-kt}\">\r<BR>\n" );
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document.write( "where k is a positive constant. The half-life is 2 hours. Assume A_0 = 1. Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 0.5 = e^{-2k} \Rightarrow -2k = \ln 0.5 \Rightarrow k = -\frac{\ln 0.5}{2} \approx. 0.3465\">\r<BR>\n" );
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document.write( "Substitute this value of k, as well as t = 1, t = 7, to find the answers to (a) and (b). </SPAN>\n" );
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