document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10298>Question 10298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I want to solve the equation:<BR>\n" );
document.write( "0.95 = exp(-a)+a*exp(-a) = exp(-a)*(1+a)\r<BR>\n" );
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document.write( "The first step I guess would be to take the natural log:<BR>\n" );
document.write( "ln(0.95) = ln(1+a)-a\r<BR>\n" );
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document.write( "Please help!<BR>\n" );
document.write( "Matt </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5440 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmaven53><B>mathmaven53(29)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmaven53><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=5440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can't solve for a algebaicly<BR>\n" );
document.write( "We try a numerical approach<BR>\n" );
document.write( " We have exp(-a)(1+a) = .95\r<BR>\n" );
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document.write( " Then 1 + a = .95 exp(a)\r<BR>\n" );
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document.write( " Plot the functions f(a) = 1+a and g(a) = .95 exp(a)\r<BR>\n" );
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document.write( " See where they intersect and estimate an approximate value of a\r<BR>\n" );
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document.write( " Call this value of a \r<BR>\n" );
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document.write( "   a_0\r<BR>\n" );
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document.write( " Try iterating values in the recursion relation \r<BR>\n" );
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document.write( " a_(n+1) = .95 exp(a_n) - 1\r<BR>\n" );
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document.write( " Note: a_0 is read a sub zero, a_(n+1)  is read a sub n plus one\r<BR>\n" );
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document.write( " When you get values of this sequence that don't differ by much then quit<BR>\n" );
document.write( "the iterations. Then you have an approximate value of a </SPAN>\n" );
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