document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865078>Question 865078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite the following equation in terms of base e. Round any natural logarithms to three decimal places. <BR>\n" );
document.write( "y=3.4(0.4)^x\r<BR>\n" );
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document.write( "Type the model in terms of base e<BR>\n" );
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document.write( "Almost done with homework! Thank you for your help! Much appreciated!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521490 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=521490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Exponential expressions with natural base e are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%2Ae%5E%28kx%29 ALIGN=MIDDLE  ALT=\"y+=+a%2Ae%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The value of 'a' is already set to be 3.4 since this is the coefficient of the given equation. We just need to find k\r<BR>\n" );
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document.write( "So set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5Ex ALIGN=MIDDLE  ALT=\"%280.4%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28kx%29 ALIGN=MIDDLE  ALT=\"e%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for k\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5Ex+=+e%5E%28kx%29 ALIGN=MIDDLE  ALT=\"%280.4%29%5Ex+=+e%5E%28kx%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=%280.4%29%5Ex+=+%28e%5Ek%29%5Ex ALIGN=MIDDLE  ALT=\"%280.4%29%5Ex+=+%28e%5Ek%29%5Ex\"   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=0.4+=+e%5Ek ALIGN=MIDDLE  ALT=\"0.4+=+e%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > The two sides have the same exponent of x. So the two bases are 0.4 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ek ALIGN=MIDDLE  ALT=\"e%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.4%29+=+k ALIGN=MIDDLE  ALT=\"ln%280.4%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert to logarithmic form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+ln%280.4%29 ALIGN=MIDDLE  ALT=\"k+=+ln%280.4%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=k+=+-0.91629073187 ALIGN=MIDDLE  ALT=\"k+=+-0.91629073187\"   DISABLED_style= \"max-width:90%; height:auto;\" > Using a <a  rel=nofollow HREF=\"https://www.google.com/search?q=ln(0.4)\">calculator</a> here.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-0.916 ALIGN=MIDDLE  ALT=\"k+=+-0.916\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round any natural logarithms to three decimal places. \r<BR>\n" );
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document.write( "This means\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28kx%29=e%5E%28-0.916x%29 ALIGN=MIDDLE  ALT=\"e%5E%28kx%29=e%5E%28-0.916x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5Ex ALIGN=MIDDLE  ALT=\"%280.4%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.916x%29 ALIGN=MIDDLE  ALT=\"e%5E%28-0.916x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to go from\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3.4%280.4%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+3.4%280.4%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3.4%2Ae%5E%28-0.916x%29 ALIGN=MIDDLE  ALT=\"y+=+3.4%2Ae%5E%28-0.916x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=============================================================\r<BR>\n" );
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document.write( "Final Answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3.4%2Ae%5E%28-0.916x%29 ALIGN=MIDDLE  ALT=\"y+=+3.4%2Ae%5E%28-0.916x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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