document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178995>Question 1178995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 20 grams of an unknown compound decays continuously according to the model A = 20e-0.02t<BR>\n" );
document.write( "where A is the amount of the compound remaining after t years. How long before the amount <BR>\n" );
document.write( "of compound reaches one-fourth of its original amount?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808486 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20 grams of an unknown compound decays continuously according to the model:<BR>\n" );
document.write( " A = 20e-0.02t where A is the amount of the compound remaining after t years.<BR>\n" );
document.write( " How long before the amount of compound reaches one-fourth of its original amount?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1/4 of 20 grams is 5 grams, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Ae%5E%28-.02t%29+=+5 ALIGN=MIDDLE  ALT=\"20%2Ae%5E%28-.02t%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-.02t%29+=+5%2F20 ALIGN=MIDDLE  ALT=\"e%5E%28-.02t%29+=+5%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-.02t%29+=+.25 ALIGN=MIDDLE  ALT=\"e%5E%28-.02t%29+=+.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using natural logs<BR>\n" );
document.write( "-.02t*ln(e) = ln(2.5)<BR>\n" );
document.write( "ln of e is 1, therefore<BR>\n" );
document.write( "-.02t = -1.3863<BR>\n" );
document.write( "t = -1.3863/-.2<BR>\n" );
document.write( "t = 69.3 years<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );