document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309586>Question 309586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you invest $2,000 at 8.5% interest compounded continuously. how long will it take for the account balance to reach $5,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221438 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=221438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     you invest $2,000 at 8.5% interest compounded continuously. how long will it take for the account balance to reach $5,000?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When you see \"continuous compounding\" think:<BR>\n" );
document.write( "A = Poe^(rt)<BR>\n" );
document.write( "where<BR>\n" );
document.write( "A is amount after time t<BR>\n" );
document.write( "Po is the initial amount<BR>\n" );
document.write( "r is the rate/interest<BR>\n" );
document.write( "t is time<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Plugging in what was given into:<BR>\n" );
document.write( "A = Poe^(rt)<BR>\n" );
document.write( "we get:<BR>\n" );
document.write( "5000 = 2000e^(.085t)<BR>\n" );
document.write( "5000/2000 = e^(.085t)<BR>\n" );
document.write( "5/2 = e^(.085t)<BR>\n" );
document.write( "ln(5/2) = .085t<BR>\n" );
document.write( "ln(5/2)/.085 = t<BR>\n" );
document.write( "10.8 years = t\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );