document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=576524>Question 576524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!!!\r<BR>\n" );
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document.write( "The half life of an element is 3.9 * 10^9 yr. How long does it take a sample of the element to decay to 2/5 of its original mass? Use A=A0(1/2)^(t/T) where AO is the initial amount, T is the half life, and t is the time. (express results in scientific notation, rounded to the nearest hundredth)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369914 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5D%281%2F2%29%5E%28t%2FT%29 ALIGN=MIDDLE  ALT=\"A=A%5B0%5D%281%2F2%29%5E%28t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation given and you want the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > that will make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FA%5B0%5D=2%2F5 ALIGN=MIDDLE  ALT=\"A%2FA%5B0%5D=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(You know it has to be more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=3.9+%2A+10%5E9years ALIGN=MIDDLE  ALT=\"T=3.9+%2A+10%5E9years\"   DISABLED_style= \"max-width:90%; height:auto;\" > because at T you would have 1/2 left and 2/5<1/2).<BR>\n" );
document.write( "We could divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D ALIGN=MIDDLE  ALT=\"A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FA%5B0%5D=%281%2F2%29%5E%28t%2FT%29 ALIGN=MIDDLE  ALT=\"A%2FA%5B0%5D=%281%2F2%29%5E%28t%2FT%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Taking logarithm of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2Alog%28%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2Alog%28%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%28log%281%29-log%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%28log%281%29-log%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%280-log%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%280-log%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%28-log%282%29%29 ALIGN=MIDDLE  ALT=\"log%28%28A%2FA%5B0%5D%29%29=%28t%2FT%29%2A%28-log%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28A%2FA%5B0%5D%29%29=-%28t%2FT%29%2Alog%282%29 ALIGN=MIDDLE  ALT=\"log%28%28A%2FA%5B0%5D%29%29=-%28t%2FT%29%2Alog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plugging in the values given,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%282%2F5%29%29=-%28t%2F%283.9+%2A+10%5E9%29%29%2Alog%282%29 ALIGN=MIDDLE  ALT=\"log%28%282%2F5%29%29=-%28t%2F%283.9+%2A+10%5E9%29%29%2Alog%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the approximate values for the logarithms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.39794=-0.30103%2At%2F%283.9+%2A+10%5E9%29 ALIGN=MIDDLE  ALT=\"-0.39794=-0.30103%2At%2F%283.9+%2A+10%5E9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.39794%2A%283.9%2A+10%5E9%29%2F0.30103 ALIGN=MIDDLE  ALT=\"t=0.39794%2A%283.9%2A+10%5E9%29%2F0.30103\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=5.16%2A10%5E9years%29 ALIGN=MIDDLE  ALT=\"highlight%28t=5.16%2A10%5E9years%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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