document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133494>Question 133494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) How long will it take for $5000.00 to grow to $15,000.00 if the annual interest rate over that time is 4.85% and continuous compounding is used? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97670 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=97670\">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=Pe%5E%28rt%29 ALIGN=MIDDLE  ALT=\"A=Pe%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15000=5000e%5E%280.0485t%29 ALIGN=MIDDLE  ALT=\"15000=5000e%5E%280.0485t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=15000 ALIGN=MIDDLE  ALT=\"A=15000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=5000 ALIGN=MIDDLE  ALT=\"P=5000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.0485 ALIGN=MIDDLE  ALT=\"r=0.0485\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29=ln%285000e%5E%280.0485t%29%29 ALIGN=MIDDLE  ALT=\"ln%2815000%29=ln%285000e%5E%280.0485t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29=ln%285000%29%2Bln%28e%5E%280.0485t%29%29 ALIGN=MIDDLE  ALT=\"ln%2815000%29=ln%285000%29%2Bln%28e%5E%280.0485t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the natural log on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29-ln%285000%29=ln%28e%5E%280.0485t%29%29 ALIGN=MIDDLE  ALT=\"ln%2815000%29-ln%285000%29=ln%28e%5E%280.0485t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%285000%29 ALIGN=MIDDLE  ALT=\"ln%285000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29-ln%285000%29=0.0485t%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%2815000%29-ln%285000%29=0.0485t%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the right side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5Ey%29=y%2Aln%28x%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%5Ey%29=y%2Aln%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29-ln%285000%29=0.0485t%2A1 ALIGN=MIDDLE  ALT=\"ln%2815000%29-ln%285000%29=0.0485t%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2815000%29-ln%285000%29=0.0485t ALIGN=MIDDLE  ALT=\"ln%2815000%29-ln%285000%29=0.0485t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ln%2815000%29-ln%285000%29%29%2F0.0485=t ALIGN=MIDDLE  ALT=\"%28ln%2815000%29-ln%285000%29%29%2F0.0485=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 0.0485 to isolate t\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using a calculator, we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=22.6517998 ALIGN=MIDDLE  ALT=\"t=22.6517998\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So it takes about 22.65 years for $5000.00 to grow to $15,000.00 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );