document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097962>Question 1097962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem: <BR>\n" );
document.write( "You are saving $590 a week to buy a new computer. Your brother is saving at a weekly rate of 4^{x-2}, if x = the number of weeks of saving. What is the first week that your brother will have more money saved than you? \r<BR>\n" );
document.write( "\n" );
document.write( "When I solved it I got 7 but then realized that each week is increasing by 590 for the person. I don't know what to do.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712418 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The \"You\" person is saving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24590%22 ALIGN=MIDDLE  ALT=\"%22%24590%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > per week,<BR>\n" );
document.write( "so after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > weeks, the saving for that person (in $) would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=590n ALIGN=MIDDLE  ALT=\"590n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The savings grow linearly.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The amounts the brother would save (in $) would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%281-2%29=4%5E%28-1%29=0.25 ALIGN=MIDDLE  ALT=\"4%5E%281-2%29=4%5E%28-1%29=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > for week 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%282-2%29=4%5E0=1 ALIGN=MIDDLE  ALT=\"4%5E%282-2%29=4%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for week 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%283-2%29=4%5E1=4 ALIGN=MIDDLE  ALT=\"4%5E%283-2%29=4%5E1=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > for week 3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%284-2%29=4%5E2=16 ALIGN=MIDDLE  ALT=\"4%5E%284-2%29=4%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > for week 4,<BR>\n" );
document.write( "and so on.<BR>\n" );
document.write( "The weekly savings form a geometric sequence<BR>\n" );
document.write( "(or geometric progression, or GP, as you wish to call it).<BR>\n" );
document.write( "The dirst term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0.25 ALIGN=MIDDLE  ALT=\"b=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the common ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=b%2A%28r%5En-1%29%2F%28r-1%29=0.25%284%5En-1%29%2F%284-1%29=0.25%284%5En-1%29%2F3=0.25%2A4%5En%2F3-0.25%2F3=4%5E%28n-1%29%2F3-0.25%2F3=%284%5E%28n-1%29-0.25%29%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The brother's savings grow exponentially.<BR>\n" );
document.write( " <BR>\n" );
document.write( "At the beginning the \"you\" person will have more saved,<BR>\n" );
document.write( "but the brother is a faster saver,<BR>\n" );
document.write( "and would soon have more saved than the you person.<BR>\n" );
document.write( " <BR>\n" );
document.write( "That would happen when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28n-1%29%2F3-0.25%2F3%3E590n ALIGN=MIDDLE  ALT=\"4%5E%28n-1%29%2F3-0.25%2F3%3E590n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It is easy to get to the answer by calculating both sides for a few values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "CALCULATING FOR A FEW <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > VALUES:<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=6 ALIGN=MIDDLE  ALT=\"n=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=590n=590%2A6=3540 ALIGN=MIDDLE  ALT=\"590n=590%2A6=3540\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%28n-1%29-0.25%29%2F3=%284%5E5-0.25%29%2F3=%281024-0.25%29%2F3=1023.75%2F3=341.25 ALIGN=MIDDLE  ALT=\"%284%5E%28n-1%29-0.25%29%2F3=%284%5E5-0.25%29%2F3=%281024-0.25%29%2F3=1023.75%2F3=341.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the brother does not have the most savings.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=8 ALIGN=MIDDLE  ALT=\"n=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=590n=590%2A8=4720 ALIGN=MIDDLE  ALT=\"590n=590%2A8=4720\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%28n-1%29-0.25%29%2F3=%284%5E7-0.25%29%2F3=%2896384-0.25%29%2F3=96383.75%2F3=5461.25 ALIGN=MIDDLE  ALT=\"%284%5E%28n-1%29-0.25%29%2F3=%284%5E7-0.25%29%2F3=%2896384-0.25%29%2F3=96383.75%2F3=5461.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the brother have more savings than the \"you\" person.<BR>\n" );
document.write( "What about for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=7 ALIGN=MIDDLE  ALT=\"n=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=7 ALIGN=MIDDLE  ALT=\"n=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=590n=590%2A7=5310 ALIGN=MIDDLE  ALT=\"590n=590%2A7=5310\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E%28n-1%29-0.25%29%2F3=%284%5E6-0.25%29%2F3=%284096-0.25%29%2F3=4095.75%2F3=1365.25 ALIGN=MIDDLE  ALT=\"%284%5E%28n-1%29-0.25%29%2F3=%284%5E6-0.25%29%2F3=%284096-0.25%29%2F3=4095.75%2F3=1365.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the \"you\" person still has nore savings than the brother.<BR>\n" );
document.write( "So the first time that the brother has more money saved than the you person is<BR>\n" );
document.write( "when the brother has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > weeks worth of savings. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );