document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167473>Question 1167473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 5500 lbs of a radioactive element with a half life of 5 years. What is its continuous decay rate? Please write your answer as a percentage using 2 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792061 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=792061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the continuous growth / decay formula is f = p * e ^ (r * t)<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "e is the scientific constant of 2.718281828 rounded to 9 decimal places.<BR>\n" );
document.write( "r is the growth / decay rate per time period.<BR>\n" );
document.write( "t is the number of time periods.\r<BR>\n" );
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document.write( "in your problem, the time period is expressed in years.\r<BR>\n" );
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document.write( "to find the rate for the half line in 5 years, do the following:\r<BR>\n" );
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document.write( "1 = 2 * e ^ (r * 5)<BR>\n" );
document.write( "divide both sides of this equation by 2 to get:<BR>\n" );
document.write( ".5 = e ^ (r * 5)<BR>\n" );
document.write( "take the natural log of both sides of this equation to get:<BR>\n" );
document.write( "ln(.5) = ln(e ^ (r * 5))<BR>\n" );
document.write( "since ln(e ^ (r * 5)) = r * 5 * ln(e), and since ln(e) = 1, the formula becomes:<BR>\n" );
document.write( "ln(.5) = r * 5<BR>\n" );
document.write( "divide both sides of this formula by 5 to get:<BR>\n" );
document.write( "ln(.5) / 5 = r<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = -.1386294361.\r<BR>\n" );
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document.write( "confirm this rate is good by replacing r in the original equation with it and solving for f.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "f = e ^ (-.1386294361 * 5)<BR>\n" );
document.write( "solve for f to get:<BR>\n" );
document.write( "f = .5\r<BR>\n" );
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document.write( "this confirms the value of r is good.\r<BR>\n" );
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document.write( "your solution is that the continuous decay rate is equal to -.1386294361 per year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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