document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184684>Question 184684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to figure out the slope and an equation for the following points.<BR>\n" );
document.write( "(1,4), (2,16), (3,64), (4,256), (5,1024), (6,4096).  I know that each time the Y value goes up by *4, but I can not figure out what the exact slope is.  Please Help!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138599 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=138599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I need to figure out the slope and an equation for the following points.<BR>\n" );
document.write( "(1,4), (2,16), (3,64), (4,256), (5,1024), (6,4096).<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "there is no consistent slope; the points are not on a line.<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The equation for these points is an exponential equation:<BR>\n" );
document.write( "y = ab^x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute a couple of points into the form:<BR>\n" );
document.write( "16 = ab^2<BR>\n" );
document.write( "4  = ab<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Divide the 2nd into the 1st to get rid of the \"a\" factor:<BR>\n" );
document.write( "4 = b<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Substitute that back into one of the equations to solve for \"a\".<BR>\n" );
document.write( "4 = a*4<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y = 4^x (this is the equation the points fit into)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Here is the graph; you can see the slope is constantly changing.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C4%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C4%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );