document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176085>Question 1176085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The half-life of cobalt - 60 is 5.27 years. Starting with a sample of 150 mg, after how many years is 20 mg left? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #802123 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=802123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the half life of cobalt-60 is 5.27 years.\r<BR>\n" );
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document.write( "to find the annual rate of decay, use the exponential formula to get:\r<BR>\n" );
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document.write( ".5 = x ^ 5.27\r<BR>\n" );
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document.write( "take the 5.27th root of both sides of this equation to get:\r<BR>\n" );
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document.write( ".5 ^ (1/5.27) = x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .8767556206\r<BR>\n" );
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document.write( "to confirm that value of x is good, replace x in the original equation and solve for y.\r<BR>\n" );
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document.write( "you get y = .8767556206 ^ 5.27 = .5\r<BR>\n" );
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document.write( "this confirms the value of x is good.\r<BR>\n" );
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document.write( "you can now use that value of x to solve the problem.\r<BR>\n" );
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document.write( "if y = 20 when x = 150, then the formula becomes:\r<BR>\n" );
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document.write( "20 = 150 * .8767556206 ^ n\r<BR>\n" );
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document.write( "divide both sides of that equation by 150 to get:\r<BR>\n" );
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document.write( "20/150 = .8767556206 ^ n\r<BR>\n" );
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document.write( "take the log of both sides of that equation to get:\r<BR>\n" );
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document.write( "log(2/15) = log(.8767556206 ^ n)\r<BR>\n" );
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document.write( "since log(x ^ a) = a * log(x), that equation becomes:\r<BR>\n" );
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document.write( "log(2/15) = n * log(.8767556206)\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = log(2/15) / log(.8767556206) = 15.31931344.\r<BR>\n" );
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document.write( "confirm by replacing n in the original equation by that value and solving for y.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "y = 150 * .8767556206 ^ 15.3191344 = 20.\r<BR>\n" );
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document.write( "that confirms the value of n is good.\r<BR>\n" );
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document.write( "15.3191344 years is your solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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