document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966341>Question 966341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 20 mg; the half-life is 200 days. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590661 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=590661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units.<BR>\n" );
document.write( " For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 20 mg; the half-life is 200 days.<BR>\n" );
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document.write( "The equation is:<BR>\n" );
document.write( "Half remains after 200 days<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+Yo%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"Y+=+Yo%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:<BR>\n" );
document.write( "Y = amt after t time (10 mg)<BR>\n" );
document.write( "Yo = initial amt (20 mg)<BR>\n" );
document.write( "k = half-life of the substance <BR>\n" );
document.write( "t = time of decay (200)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Ae%5E%28200k%29+=+10 ALIGN=MIDDLE  ALT=\"20%2Ae%5E%28200k%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28200k%29+=+10%2F20 ALIGN=MIDDLE  ALT=\"e%5E%28200k%29+=+10%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28200k%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"e%5E%28200k%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ln of e is 1, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200k+=+ln%281%2F2%29 ALIGN=MIDDLE  ALT=\"200k+=+ln%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "200k = -.693147<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.693147%2F200 ALIGN=MIDDLE  ALT=\"-.693147%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = -.0034657<BR>\n" );
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document.write( "Check this on your calc: 20*e^(-.0034657*200) = 10.000 </SPAN>\n" );
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