document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150903>Question 1150903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vanessa, the student council president, needed to get a message to the whole school, so she set up an email tree. She sent the message to the two vice presidents and made them forward it to two other students. Suppose the pattern is repeated and no student receives it more than once!\r<BR>\n" );
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document.write( "a) How many people receive it during the seventh mailing?<BR>\n" );
document.write( "b) Which mailing will be sent to 500 people?<BR>\n" );
document.write( "c) There are 500 students in the school, so how many does it take to send the mail to all of them? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772467 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two components here, how many receive the new email in a round, and the total of students that have been informed.\r<BR>\n" );
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document.write( "Each time an email is sent, it reaches <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=twice ALIGN=MIDDLE  ALT=\"twice\"   DISABLED_style= \"max-width:90%; height:auto;\" > as many people as the time before.  So the pattern is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4 ALIGN=MIDDLE  ALT=\"+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8 ALIGN=MIDDLE  ALT=\"+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128 ALIGN=MIDDLE  ALT=\"128\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+256 ALIGN=MIDDLE  ALT=\"+256\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512 ALIGN=MIDDLE  ALT=\"512\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.  \r<BR>\n" );
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document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <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 a particular <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=round ALIGN=MIDDLE  ALT=\"round\"   DISABLED_style= \"max-width:90%; height:auto;\" > of mailing.\r<BR>\n" );
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document.write( "Now when this starts, Vanessa knows, that's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > person.  After the first mailing, it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B1 ALIGN=MIDDLE  ALT=\"2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > people that know, next it's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B2%2B1 ALIGN=MIDDLE  ALT=\"4%2B2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2B4%2B2%2B1 ALIGN=MIDDLE  ALT=\"+8%2B4%2B2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.  You might recognize this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28n%2B1%29+-+1 ALIGN=MIDDLE  ALT=\"2%5E%28n%2B1%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "a)  How many people receive it during the 7th mailing?\r<BR>\n" );
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document.write( "use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <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 a particular <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=round ALIGN=MIDDLE  ALT=\"round\"   DISABLED_style= \"max-width:90%; height:auto;\" > of mailing\r<BR>\n" );
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document.write( "so, in your case <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En=2%5E7+=+128+ ALIGN=MIDDLE  ALT=\"2%5En=2%5E7+=+128+\"   DISABLED_style= \"max-width:90%; height:auto;\" >people\r<BR>\n" );
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document.write( "b) Which mailing will be sent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500 ALIGN=MIDDLE  ALT=\"500\"   DISABLED_style= \"max-width:90%; height:auto;\" > people?\r<BR>\n" );
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document.write( "Since we already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7+=+128 ALIGN=MIDDLE  ALT=\"2%5E7+=+128\"   DISABLED_style= \"max-width:90%; height:auto;\" >, let's keep going from there.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7=128 ALIGN=MIDDLE  ALT=\"2%5E7=128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E8+=+128+%2A+2+=+256 ALIGN=MIDDLE  ALT=\"2%5E8+=+128+%2A+2+=+256\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E9=+256+%2A2+=+512 ALIGN=MIDDLE  ALT=\"2%5E9=+256+%2A2+=+512\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we have exceeded <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500 ALIGN=MIDDLE  ALT=\"500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we stop there. \r<BR>\n" );
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document.write( "So, we know that since the power is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the email has been sent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.\r<BR>\n" );
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document.write( "c) There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500+ ALIGN=MIDDLE  ALT=\"500+\"   DISABLED_style= \"max-width:90%; height:auto;\" >students in the school, so how many does it take to send the mail to all of them?\r<BR>\n" );
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document.write( "This question was already answered in part b). The answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512 ALIGN=MIDDLE  ALT=\"512\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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