document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284179>Question 284179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help me with this problem? Use the formula N = Ie^kt, where N is the number of items in terms of the initial population I, at time T, and k is the growth constant equal to the percent of growth per unit of time. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope to the nearest year. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206201 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=206201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the formula N = Ie^kt, where N is the number of items in terms of the initial population I, at time T, and k is the growth constant equal to the percent of growth per unit of time. A certain radioactive isotope decays at a rate of 0.275% annually. Determine the half-life of this isotope to the nearest year.<BR>\n" );
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document.write( "Note: Since this is a decay function I believe you need a negative<BR>\n" );
document.write( "in the exponent.<BR>\n" );
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document.write( "Substitute and solve for \"t\":<BR>\n" );
document.write( "(I/2) = I*e^(-0.275t)<BR>\n" );
document.write( "(1/2) = e^(-0.275t)<BR>\n" );
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document.write( "Take the natural log to get:<BR>\n" );
document.write( "-0.275t = ln(1/2)<BR>\n" );
document.write( "t = -0.6931../-0.275<BR>\n" );
document.write( "t = 2.52 years<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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