document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212012>Question 212012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long will it take a sample of radioactive substance to decay half of its original amount, if it decays according to the function  A(t) = 450e^-0.249t , where t is the time in years?  Round to the nearest hundreth year.\r<BR>\n" );
document.write( "\n" );
document.write( "choices (in years):<BR>\n" );
document.write( "2.78<BR>\n" );
document.write( "112.05<BR>\n" );
document.write( "24.54<BR>\n" );
document.write( "27.32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160131 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=160131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How long will it take a sample of radioactive substance to decay half of its<BR>\n" );
document.write( " original amount, if it decays according to the function <BR>\n" );
document.write( "A(t) = 450e^-0.249t , where t is the time in years? <BR>\n" );
document.write( "Round to the nearest hundredth year.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Half of original amt: 450/2 = 225 [A(t)]<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=450%2Ae%5E%28-.249t%29 ALIGN=MIDDLE  ALT=\"450%2Ae%5E%28-.249t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 225<BR>\n" );
document.write( "divide both sides by 450<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-.249t%29 ALIGN=MIDDLE  ALT=\"e%5E%28-.249t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2F450 ALIGN=MIDDLE  ALT=\"225%2F450\"   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%28-.249t%29 ALIGN=MIDDLE  ALT=\"e%5E%28-.249t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5<BR>\n" );
document.write( "then log equiv of exponents<BR>\n" );
document.write( "-.249t*ln(e) = ln(.5)<BR>\n" );
document.write( "ln of e is one so we have:<BR>\n" );
document.write( "-.249t = -.693<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.693%29%2F%28-.249%29 ALIGN=MIDDLE  ALT=\"%28-.693%29%2F%28-.249%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 2.78 yrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution on a calc; enter: 450*e^(-.249*2.78)= 225.2 half the original amt </SPAN>\n" );
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