document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253874>Question 253874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> beryllium-11 decomposes into boron-11 with a half life of 13.8 seconds.  How long will it take 240 g of beryllium-11 to decompose into 7.5g of beryllium-11? \r<BR>\n" );
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document.write( "based on the forumula provided in the text book C(t)=C(0)2e^-t/h\r<BR>\n" );
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document.write( "where C(0) = 240, C(t)=7.5 ,h=13.8\r<BR>\n" );
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document.write( "7.5/240=2e^-t/13.8\r<BR>\n" );
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document.write( "this was a s far as i got </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186255 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation to work with is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bt%5D=C%5B0%5D%2A2%2Ae%5E%28-t%2Fh%29 ALIGN=MIDDLE  ALT=\"C%5Bt%5D=C%5B0%5D%2A2%2Ae%5E%28-t%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The exponent in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2Fh ALIGN=MIDDLE  ALT=\"-t%2Fh\"   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=C%5B0%5D+=+240 ALIGN=MIDDLE  ALT=\"C%5B0%5D+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bt%5D+=+7.5 ALIGN=MIDDLE  ALT=\"C%5Bt%5D+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+13.8 ALIGN=MIDDLE  ALT=\"h+=+13.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substituting in that equation, you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5+=+240+%2A+2+%2A+e%5E%28-t%2F13.8%29 ALIGN=MIDDLE  ALT=\"7.5+=+240+%2A+2+%2A+e%5E%28-t%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the exponent in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F13.8%29 ALIGN=MIDDLE  ALT=\"-t%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you want to isolate the exponential term on the right hand side of the equation so you need to divide both sides of the equation by 240 * 2 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5%2F%282%2A240%29+=+e%5E%28-t%2F13.8%29 ALIGN=MIDDLE  ALT=\"7.5%2F%282%2A240%29+=+e%5E%28-t%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the exponent in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F13.8%29 ALIGN=MIDDLE  ALT=\"-t%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287.5%2F%282%2A240%29%29+=+log%28e%5E%28-t%2F13.8%29%29 ALIGN=MIDDLE  ALT=\"log%287.5%2F%282%2A240%29%29+=+log%28e%5E%28-t%2F13.8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since log(b^c) = c*log(b), your equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287.5%2F%282%2A240%29%29+=+%28-t%2F13.8%29+%2A+log%28e%29 ALIGN=MIDDLE  ALT=\"log%287.5%2F%282%2A240%29%29+=+%28-t%2F13.8%29+%2A+log%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply both sides of this equation by 13.8 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.8%2Alog%287.5%2F%282%2A240%29%29+=+-t%2Alog%28e%29 ALIGN=MIDDLE  ALT=\"13.8%2Alog%287.5%2F%282%2A240%29%29+=+-t%2Alog%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide both sides of this equation by -log(e) to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2813.8%2Alog%287.5%2F%282%2A240%29%29%29%2F%28-log%28e%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2813.8%2Alog%287.5%2F%282%2A240%29%29%29%2F%28-log%28e%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for t to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-24.92528364%2F-.434294482+=+57.39258655 ALIGN=MIDDLE  ALT=\"t+=+-24.92528364%2F-.434294482+=+57.39258655\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.\r<BR>\n" );
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document.write( "substitute in original equation to see if this value for t is good.\r<BR>\n" );
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document.write( "original equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bt%5D=C%5B0%5D%2A2%2Ae%5E%28-t%2Fh%29 ALIGN=MIDDLE  ALT=\"C%5Bt%5D=C%5B0%5D%2A2%2Ae%5E%28-t%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "exponent in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2Fh ALIGN=MIDDLE  ALT=\"-t%2Fh\"   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=C%5B0%5D+=+240 ALIGN=MIDDLE  ALT=\"C%5B0%5D+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bt%5D+=+7.5 ALIGN=MIDDLE  ALT=\"C%5Bt%5D+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+13.8 ALIGN=MIDDLE  ALT=\"h+=+13.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 57.39258655\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5=240%2A2%2Ae%5E%28-57.39258655%2F13.8%29 ALIGN=MIDDLE  ALT=\"7.5=240%2A2%2Ae%5E%28-57.39258655%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "exponent in the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-57.39258655%2F13.8%29 ALIGN=MIDDLE  ALT=\"%28-57.39258655%2F13.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5=480%2Ae%5E%28-4.158883083%29 ALIGN=MIDDLE  ALT=\"7.5=480%2Ae%5E%28-4.158883083%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5+=+7.5 ALIGN=MIDDLE  ALT=\"7.5+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the equation is true, the value for t is good.\r<BR>\n" );
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document.write( "t = 57.39258655 seconds<BR>\n" );
document.write( " </SPAN>\n" );
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