document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=367073>Question 367073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=1000(2raised to the -.1x)<BR>\n" );
document.write( "if x=10, what is y=?<BR>\n" );
document.write( "then, if y=250, what is x=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #261927 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=261927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1000%282%5E%28-0.1x%29%29 ALIGN=MIDDLE  ALT=\"y=1000%282%5E%28-0.1x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It help to rewrite this with a positive exponent. In general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28-p%29+=+1%2Fa%5Ep ALIGN=MIDDLE  ALT=\"a%5E%28-p%29+=+1%2Fa%5Ep\"   DISABLED_style= \"max-width:90%; height:auto;\" >. so your expression can be rewritten as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1000%281%2F2%5E%280.1x%29%29 ALIGN=MIDDLE  ALT=\"y=1000%281%2F2%5E%280.1x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "if x = 10...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1000%281%2F2%5E%280.1%2810%29%29%29 ALIGN=MIDDLE  ALT=\"y=1000%281%2F2%5E%280.1%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1000%281%2F2%5E1%29 ALIGN=MIDDLE  ALT=\"y=1000%281%2F2%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1000%281%2F2%29 ALIGN=MIDDLE  ALT=\"y=1000%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+500 ALIGN=MIDDLE  ALT=\"y+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "if y = 250...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250=1000%281%2F2%5E%280.1x%29%29 ALIGN=MIDDLE  ALT=\"250=1000%281%2F2%5E%280.1x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 1000:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250%2F1000=%281000%281%2F2%5E%280.1x%29%29%29%2F1000 ALIGN=MIDDLE  ALT=\"250%2F1000=%281000%281%2F2%5E%280.1x%29%29%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4=1%2F2%5E%280.1x%29 ALIGN=MIDDLE  ALT=\"1%2F4=1%2F2%5E%280.1x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a proportion so we can cross multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A2%5E%280.1x%29+=+4%2A1 ALIGN=MIDDLE  ALT=\"1%2A2%5E%280.1x%29+=+4%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%280.1x%29+=+4 ALIGN=MIDDLE  ALT=\"2%5E%280.1x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The shortest way to solving for x here is to recognize that both sides of the equation are powers of two:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%280.1x%29+=+2%5E2 ALIGN=MIDDLE  ALT=\"2%5E%280.1x%29+=+2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Note: If both sides had not both been powers of the same number, then we would have to use logarithms to solve for x.)<BR>\n" );
document.write( "The only way for powers of 2 to be equal is if their exponents are equal. So:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1x+=+2 ALIGN=MIDDLE  ALT=\"0.1x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And finally we can multiply both sides by 10:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%280.1x%29+=+10%282%29 ALIGN=MIDDLE  ALT=\"10%280.1x%29+=+10%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );