document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127693>Question 1127693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the formula for an exponential function that passes through the two points given.<BR>\n" );
document.write( "a) (-1,1/2) and (4,512)<BR>\n" );
document.write( "b) (-1,7) and (3,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744179 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=744179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>(NOTE: You can ignore the solution by tutor MathLover1; the question asks for exponential functions -- not linear functions.)<br><BR>\n" );
document.write( "The general form of an exponential function is<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( "Given two points on the graph of an exponential function, the general process for finding the function is<br><BR>\n" );
document.write( "(1) use the coordinates of the two given points in the general form to get two equations in x and y;<BR>\n" );
document.write( "(2) divide one equation by the other; that will eliminate a and give you an equation you can solve for b; and<BR>\n" );
document.write( "(3) use the value of b in either equation to find the value of a<br><BR>\n" );
document.write( "Your example (a) turns out to have \"nice\" numbers; so I will demonstrate the process with the second example.<br><BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%5E%28-1%29+=+7 ALIGN=MIDDLE  ALT=\"ab%5E%28-1%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%5E3+=+4 ALIGN=MIDDLE  ALT=\"ab%5E3+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E4+=+4%2F7 ALIGN=MIDDLE  ALT=\"b%5E4+=+4%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%284%2F7%29%5E%281%2F4%29+=+.86944 ALIGN=MIDDLE  ALT=\"b+=+%284%2F7%29%5E%281%2F4%29+=+.86944\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 5 decimal places<br><BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28.86944%29%5E%28-1%29+=+7 ALIGN=MIDDLE  ALT=\"a%28.86944%29%5E%28-1%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+7%28.86944%29+=+6.08608 ALIGN=MIDDLE  ALT=\"a+=+7%28.86944%29+=+6.08608\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The exponential function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6.08608%280.86944%29%5Ex ALIGN=MIDDLE  ALT=\"y+=+6.08608%280.86944%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );