document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155242>Question 1155242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a possible formula for the exponential function through the points (−2,54) and (2,6/9) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777798 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ab%5Ex ALIGN=MIDDLE  ALT=\"y+=+ab%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the two given data points:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54+=+ab%5E%28-2%29 ALIGN=MIDDLE  ALT=\"54+=+ab%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+ab%5E2 ALIGN=MIDDLE  ALT=\"2%2F3+=+ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Divide the second equation by the first:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F81+=+b%5E4 ALIGN=MIDDLE  ALT=\"1%2F81+=+b%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3+=+b ALIGN=MIDDLE  ALT=\"1%2F3+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note if this were a geometric sequence problem, the value of b could be either 1/3 or -1/3.  But for an exponential function, b has to be positive.<br><BR>\n" );
document.write( "Substitute this value of b in either original equation to find a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+a%281%2F3%29%5E2 ALIGN=MIDDLE  ALT=\"2%2F3+=+a%281%2F3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+a%2F9 ALIGN=MIDDLE  ALT=\"2%2F3+=+a%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+9%282%2F3%29+=+6 ALIGN=MIDDLE  ALT=\"a+=+9%282%2F3%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: One possible function for the two given points is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6%281%2F3%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+6%281%2F3%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );