document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703336>Question 703336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many years will it take for a $100 investment to grow to $700 if it is compounded continuously at a rate of 9%?<BR>\n" );
document.write( "A(t)= P*e^rt<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433443 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=433443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<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 continuous compounding formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700=100%2Ae%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"700=100%2Ae%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=700 ALIGN=MIDDLE  ALT=\"A=700\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=100 ALIGN=MIDDLE  ALT=\"P=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.09 ALIGN=MIDDLE  ALT=\"r=0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the decimal equivalent of 9%).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2F100=e%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"700%2F100=e%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=e%5E%280.09%2At%29 ALIGN=MIDDLE  ALT=\"7=e%5E%280.09%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2F100 ALIGN=MIDDLE  ALT=\"700%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%287%29=ln%28e%5E%280.09%2At%29%29 ALIGN=MIDDLE  ALT=\"ln%287%29=ln%28e%5E%280.09%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%287%29=0.09%2At%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%287%29=0.09%2At%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pull down the exponent 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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%287%29=0.09%2At%2A1 ALIGN=MIDDLE  ALT=\"ln%287%29=0.09%2At%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of 'e' to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%287%29=0.09%2At ALIGN=MIDDLE  ALT=\"ln%287%29=0.09%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.94591014905531=0.09%2At ALIGN=MIDDLE  ALT=\"1.94591014905531=0.09%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.94591014905531 ALIGN=MIDDLE  ALT=\"1.94591014905531\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this value is approximate).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.94591014905531%2F0.09=t ALIGN=MIDDLE  ALT=\"1.94591014905531%2F0.09=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.09 ALIGN=MIDDLE  ALT=\"0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate 't'.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.6212238783924=t ALIGN=MIDDLE  ALT=\"21.6212238783924=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.94591014905531%2F0.09 ALIGN=MIDDLE  ALT=\"1.94591014905531%2F0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.6212238783924 ALIGN=MIDDLE  ALT=\"21.6212238783924\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=21.6212238783924 ALIGN=MIDDLE  ALT=\"t=21.6212238783924\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=22 ALIGN=MIDDLE  ALT=\"t=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest whole year.\r<BR>\n" );
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document.write( "So it will take about 22 years. </SPAN>\n" );
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