document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043740>Question 1043740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me fill in the blanks:<BR>\n" );
document.write( "Andrew and Bobby both opened restaurants at the same time. Andrew reported that on the first week after opening his restaurant, he had a profit of $500, and every week after that, his profit continually increased by 12%. Bobby reported that on the first week after opening his restaurant, he had a profit of $600, and every week after that, his profit continually increased by 8%.\r<BR>\n" );
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document.write( "Use the information given above to determine how long Bobby will have a higher profit than Andrew.\r<BR>\n" );
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document.write( "The first week Andrew will have a higher profit than Bobby will occur ___ weeks after he opens his restaurant.\r<BR>\n" );
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document.write( "The first week when Andrew's profit is higher than Bobby's, Bobby starts an advertising campaign that makes his weekly profit begin to increase by 15%. Taking this change into account, what will Bobby's weekly profit be 14 weeks after opening his restaurant? ___ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658918 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = profit 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 <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the amount of the 1st weeks profit<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = weekly increase in profit<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "The equation for both of them is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+A%2A%28+1+%2B+r+%29%5En+ ALIGN=MIDDLE  ALT=\"+P+=+A%2A%28+1+%2B+r+%29%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Andrew's equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+500%2A%28+1+%2B+.12+%29%5En+ ALIGN=MIDDLE  ALT=\"+P+=+500%2A%28+1+%2B+.12+%29%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Bobby's equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+600%2A%28+1+%2B+.08+%29%5En+ ALIGN=MIDDLE  ALT=\"+P+=+600%2A%28+1+%2B+.08+%29%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Note that the 1st week for each will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+0+ ALIGN=MIDDLE  ALT=\"+n+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the week when their profits are equal<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500%2A%28+1+%2B+.12+%29%5En+=+600%2A%28+1+%2B+.08+%29%5En+ ALIGN=MIDDLE  ALT=\"+500%2A%28+1+%2B+.12+%29%5En+=+600%2A%28+1+%2B+.08+%29%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500%2A1.12%5En+=+600%2A1.08%5En+ ALIGN=MIDDLE  ALT=\"+500%2A1.12%5En+=+600%2A1.08%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.12%5En+%2F+1.08%5En+=+600%2F500+ ALIGN=MIDDLE  ALT=\"+1.12%5En+%2F+1.08%5En+=+600%2F500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+1.12%2F1.08+%29%5En+=+1.2+ ALIGN=MIDDLE  ALT=\"+%28+1.12%2F1.08+%29%5En+=+1.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the log of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2Alog%28+1.12%2F1.08+%29+=+log%28+1.2+%29%0D%0A%7B%7B%7B+n%2A%28+log%28+1.12+%29+-+log%28+1.08+%29+%29+=+log%28+1.2+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2A%28+.049218+-+.033424+%29+=+.079181+ ALIGN=MIDDLE  ALT=\"+n%2A%28+.049218+-+.033424+%29+=+.079181+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.015794n+=+.079181+ ALIGN=MIDDLE  ALT=\"+.015794n+=+.079181+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+5.01336+ ALIGN=MIDDLE  ALT=\"+n+=+5.01336+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "If I start with week <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2B+1+=+6+ ALIGN=MIDDLE  ALT=\"+5+%2B+1+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > weeks, they<BR>\n" );
document.write( "make the same profit, so<BR>\n" );
document.write( "The first week Andrew will have a higher profit than Bobby will occur 7 weeks after he opens his restaurant. <BR>\n" );
document.write( "--------------------------------------------<BR>\n" );
document.write( "After 7 weeks, Bobby's profit is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+600%2A%28+1+%2B+.08+%29%5E6+ ALIGN=MIDDLE  ALT=\"+P+=+600%2A%28+1+%2B+.08+%29%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( 1st week is week <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+600%2A1.08%5E6+ ALIGN=MIDDLE  ALT=\"+P+=+600%2A1.08%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+600%2A+1.58687+ ALIGN=MIDDLE  ALT=\"+P+=+600%2A+1.58687+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+952.12+ ALIGN=MIDDLE  ALT=\"+P+=+952.12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then Bobby's equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+952.12%2A%28+1+%2B+.15+%29%5En+ ALIGN=MIDDLE  ALT=\"+P+=+952.12%2A%28+1+%2B+.15+%29%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" > is now from <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+13+ ALIGN=MIDDLE  ALT=\"+n+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is 7 weeks, but the 1st week is week <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+952.12%2A%28+1+%2B+.15+%29%5E6+ ALIGN=MIDDLE  ALT=\"+P+=+952.12%2A%28+1+%2B+.15+%29%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+952.12%2A1.15%5E6+ ALIGN=MIDDLE  ALT=\"+P+=+952.12%2A1.15%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+952.12%2A2.31306+ ALIGN=MIDDLE  ALT=\"+P+=+952.12%2A2.31306+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2202.31 ALIGN=MIDDLE  ALT=\"+P+=+2202.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What is Bobby's weekly profit 14 weeks after opening his restaurant? <BR>\n" );
document.write( "$2,202.31<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "I could easily get this wrong.<BR>\n" );
document.write( "Get another opinion, too. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );