document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=841236>Question 841236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you get an exponential equation from this points (0,4), (1,6), (2,9), (3,14), (4,21) and (5,31)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #506715 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=506715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plot the points on graph paper, but FIRST, TAKE THE LOGARITHMS OF THE y-coordinate VALUES!  Pick either base e or base 10, one or the other; not both.  You are looking for a line this way:\r<BR>\n" );
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document.write( "(Using Natural Logs as an example)<BR>\n" );
document.write( "Imagine you have ordered pairs of the form, (x,y).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ae%5E%28kx%29 ALIGN=MIDDLE  ALT=\"y=ae%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29=ln%28ae%5E%28kx%29%29 ALIGN=MIDDLE  ALT=\"ln%28y%29=ln%28ae%5E%28kx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29=ln%28a%29%2Bkx%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28y%29=ln%28a%29%2Bkx%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29=ln%28a%29%2Bkx ALIGN=MIDDLE  ALT=\"ln%28y%29=ln%28a%29%2Bkx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28ln%28y%29=kx%2Bln%28a%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28ln%28y%29=kx%2Bln%28a%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a linear equation, and your set of points might very well fit this model.  The vertical axis is for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29 ALIGN=MIDDLE  ALT=\"ln%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the horizontal axis is  for x values, the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the vertical axis intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28a%29 ALIGN=MIDDLE  ALT=\"ln%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "When you then want this back in the form of an exponential equation, setup your ln(y) equation with the k and intercept you found, and work backward using algebraic steps toward getting y as a function of x.<BR>\n" );
document.write( "---- Better yet, once you have the values, just use them to directly form the exponential equation. </SPAN>\n" );
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