document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979663>Question 979663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost C of a pound of a margarine in 2006 was 66 cents. in 2010 the cost was 83 cents. assuming the exponential growth model applies:\r<BR>\n" );
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document.write( "A: Find the exponential growth rate to the nearest tenth of a percent, and write the equation.\r<BR>\n" );
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document.write( "B: Find the cost of a pound of margarine in 2012 and 2018 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600957 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</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=600957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You may have a choice of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=pb%5Ex ALIGN=MIDDLE  ALT=\"C=pb%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=pe%5E%28kx%29 ALIGN=MIDDLE  ALT=\"C=pe%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You can use any base b you want, which may be 10, or 2, or e, and the initial cost for a pound is the variable p.  e is the base of the Natural Logarithm, for the second choice of equation model, which will involve a constant k as part of the exponent.\r<BR>\n" );
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document.write( "Which form of the model?  Your choice.\r<BR>\n" );
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document.write( "This help posting will use the first one.<BR>\n" );
document.write( "EITHER base you like, find logarithm of both sides.  I will use natural log base just for convenience.  You use base ten, if you want.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28C%29=ln%28pb%5Ex%29 ALIGN=MIDDLE  ALT=\"ln%28C%29=ln%28pb%5Ex%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%28C%29=ln%28p%29%2Bln%28b%5Ex%29 ALIGN=MIDDLE  ALT=\"ln%28C%29=ln%28p%29%2Bln%28b%5Ex%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%28C%29=ln%28p%29%2Bx%2Aln%28b%29 ALIGN=MIDDLE  ALT=\"ln%28C%29=ln%28p%29%2Bx%2Aln%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28ln%28C%29=ln%28b%29%2Ax%2Bln%28p%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28ln%28C%29=ln%28b%29%2Ax%2Bln%28p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------This is a linear equation having slope  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28b%29 ALIGN=MIDDLE  ALT=\"ln%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and vertical axis intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29 ALIGN=MIDDLE  ALT=\"ln%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The points to use for this linear form need to use natural log of the costs, because the linear equation defines a formula for the natural log of cost.\r<BR>\n" );
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document.write( "The ordered pairs for your points are   (2006, ln(66)) and  (2010, ln(83)).\r<BR>\n" );
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document.write( "You already have learned what to do with a system of two linear equations.  Using each pair of points gives a corresponding equation, and the new unknowns to solve for will be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28b%29 ALIGN=MIDDLE  ALT=\"ln%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for slope and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29 ALIGN=MIDDLE  ALT=\"ln%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for vertical axis intercept. </SPAN>\n" );
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