document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193252>Question 193252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if $350 is deposited in an account paying 2% annual interest, compunded continuously, how long will it take for the account to increase to $1500?\r<BR>\n" );
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document.write( "A=Pe^rt\r<BR>\n" );
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document.write( "1500=350e^.02(t)\r<BR>\n" );
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document.write( "then im lost... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145084 by </B><A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><B>MathGuyJoe(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><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=145084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To Solve:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500=350e%5E%28.02t%29 ALIGN=MIDDLE  ALT=\"1500=350e%5E%28.02t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You must first isolate the e^x component -- so divide both sides by 350:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1500+%2F+350+=+e%5E%28.02t%29+ ALIGN=MIDDLE  ALT=\"+1500+%2F+350+=+e%5E%28.02t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying gives you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+%2F+7+=+e%5E%28.02t%29+ ALIGN=MIDDLE  ALT=\"+30+%2F+7+=+e%5E%28.02t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, take the natural log (ln) 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%2830%2F7%29+=+ln%28e%5E%28.02t%29%29+ ALIGN=MIDDLE  ALT=\"+ln%2830%2F7%29+=+ln%28e%5E%28.02t%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, use the power rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28x%29%5En+=+n+%2A+ln%28x%29+ ALIGN=MIDDLE  ALT=\"+ln%28x%29%5En+=+n+%2A+ln%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to simplify the right side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%2830%2F7%29+=+.02t%2Aln%28e%29+ ALIGN=MIDDLE  ALT=\"+ln%2830%2F7%29+=+.02t%2Aln%28e%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28e%29+=+1+ ALIGN=MIDDLE  ALT=\"+ln%28e%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you're left with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%2830%2F7%29+=+.02t+ ALIGN=MIDDLE  ALT=\"+ln%2830%2F7%29+=+.02t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by .02 to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28ln%2830%2F7%29%2F.02%29+=+t+ ALIGN=MIDDLE  ALT=\"+%28ln%2830%2F7%29%2F.02%29+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<font color=\"blue\">So t = 72.76 years</font><BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
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document.write( "~ Joe </SPAN>\n" );
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