document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818780>Question 818780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493253 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=493253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.\r<BR>\n" );
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document.write( "y=ax^n - 23 and that y=4 when x=3 and y=220 when x=9 find the value of a and n.\r<BR>\n" );
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document.write( "4 = a(3)^n  <BR>\n" );
document.write( "and <BR>\n" );
document.write( "220 = a(9)^n\r<BR>\n" );
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document.write( "Let's solve each equation for a<BR>\n" );
document.write( "4 = a(3)^n<BR>\n" );
document.write( "divide each side by (3)^n an we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"a=4%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly 220 = a(9)^n can be written<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=220%2F%28%289%29%5En%29 ALIGN=MIDDLE  ALT=\"a=220%2F%28%289%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Setting the right hand sides to be equal,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"4%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220%2F%28%289%29%5En%29 ALIGN=MIDDLE  ALT=\"220%2F%28%289%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Taking the cross products we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28%289%29%5En%29 ALIGN=MIDDLE  ALT=\"4%2A%28%289%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220%2A%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"220%2A%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide each side by 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%289%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220%2F4%29%2A%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"%28220%2F4%29%2A%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%289%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2A%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"55%2A%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide each side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289%29%5En%29%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%289%29%5En%29%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55 ALIGN=MIDDLE  ALT=\"55\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5E2%29%5En%29%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%283%5E2%29%5En%29%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55 ALIGN=MIDDLE  ALT=\"55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%5En%29%5E2%29%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"%28%283%5En%29%5E2%29%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55 ALIGN=MIDDLE  ALT=\"55\"   DISABLED_style= \"max-width:90%; height:auto;\" >So,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5En ALIGN=MIDDLE  ALT=\"%283%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55 ALIGN=MIDDLE  ALT=\"55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the log of each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"log%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2855%29 ALIGN=MIDDLE  ALT=\"log%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Alog%28%283%29%29 ALIGN=MIDDLE  ALT=\"n%2Alog%28%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2855%29 ALIGN=MIDDLE  ALT=\"log%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide each side by log(3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%2855%29%29%2F%28log%283%29%29 ALIGN=MIDDLE  ALT=\"%28log%2855%29%29%2F%28log%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=3.647632<BR>\n" );
document.write( "Now substitute in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2F%28%283%29%5En%29 ALIGN=MIDDLE  ALT=\"a=4%2F%28%283%29%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2F%28%283%29%5E3.647632%29 ALIGN=MIDDLE  ALT=\"a=4%2F%28%283%29%5E3.647632%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2F%2855%29 ALIGN=MIDDLE  ALT=\"a=4%2F%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=0.072727<BR>\n" );
document.write( "Let's check the second equation, 220 = a(9)^n<BR>\n" );
document.write( "220 ?= (0.072727)(9^3.647632)<BR>\n" );
document.write( "220 ?= (0.072727)(3025.001)<BR>\n" );
document.write( "     = 219.9992   So considering rounding error we seem to be correct. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );