document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359107>Question 359107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The weight Wt grams, of radioactive substance remaining after t years is given by Wt=1000*2^-0.04t grams. Find the time taken for the weight to:<BR>\n" );
document.write( "a. halve<BR>\n" );
document.write( "b. reach 1% of its original value\r<BR>\n" );
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document.write( "Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256272 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Your function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ W(t)\ =\ 1000\,\cdot\,2^{-0.04t}\">\r<BR>\n" );
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document.write( "is only valid if you start with a kilogram of a particular substance.  The correct general formula for that particular substance is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ W(t)\ =\ W_o\,\cdot\,2^{-0.04t}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large W_o\"> is the starting weight of the substance.\r<BR>\n" );
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document.write( "If we are interested in the time for the weight to halve, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{W(t)}{W_o}\ =\ \frac{1}{2}\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2^{-0.04t}\ =\ 0.5\">\r<BR>\n" );
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document.write( "Take the log of both sides (any base is ok, but you should use either base 10 or base e because those are generally what is supported by your calculator)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ln\left(2^{-0.04t}\right)\ =\ \ln(0.5)\">\r<BR>\n" );
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document.write( "Use the laws of logarithms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ -0.04t\ln\left(2\right)\ =\ \ln(0.5)\">\r<BR>\n" );
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document.write( "Divide by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -0.04\ln(2)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(0.5)}{-0.04\ln\left(2\right)}\">\r<BR>\n" );
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document.write( "The rest is calculator work.\r<BR>\n" );
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document.write( "Part b is done the same way, except:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{W(t)}{W_o}\ =\ 0.01\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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