document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136743>Question 1136743</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( " Your	boss	offers	you	a	ten-day	job	with	three	choices	for	how	to	be	paid.		Option	#1	says	that	you	will	receive	$1	the	first	day,	$2	the	second	day,	$3	the	third	day,	and	so	on.		Option	#2	says	you	will	receive	10₵	the	first	day,	20₵	the	second	day,	40₵	the	third	day,	80₵	the	fourth	day,	and	so	on.		Option	#3	says	that	you	will	receive	$6	a	day	for	all	ten	days.which option should u choose if u want to make most amount of money? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754540 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> with option 1, you would get paid 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 dollars.\r<BR>\n" );
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document.write( "with option 2, you would get paid .1 + .2 + .4 + .8 + 1.6 + 3.2 + 6.4 + 12.8 + 25.6 + 51.2 = 102.3 dollars.\r<BR>\n" );
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document.write( "with option 3, you would get paid 6 * 10 = 60 dollars.\r<BR>\n" );
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document.write( "looks like option 2 needs to be your choice if you want to make the most money.\r<BR>\n" );
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document.write( "option 2 is a geometric series.\r<BR>\n" );
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document.write( "the formula is An = A1 * r ^ (n-1).\r<BR>\n" );
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document.write( "A1 is .1<BR>\n" );
document.write( "r is 2 because it doubles every time.<BR>\n" );
document.write( "n is 10.\r<BR>\n" );
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document.write( "the formula becomes A10 = .1 * 2 ^ 9 = 51.2.\r<BR>\n" );
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document.write( "that's what you make on the 10th day.\r<BR>\n" );
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document.write( "the sum of a geometric series is Sn = A1 * (1 - r^n) / (1 - r)\r<BR>\n" );
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document.write( "in this problem, that becomes S10 = .1 * (1 - 2^10) / (1 - 2) which becomes S10 = .1 * (-1023) / -1 which becomes -102.3 / -1 which 102.3.\r<BR>\n" );
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document.write( "that'w what we got above when we added each of the individual terms manually.\r<BR>\n" );
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document.write( "anyway, option 2 is your best bet.\r<BR>\n" );
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document.write( "you make the most money with that option.\r<BR>\n" );
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document.write( "all that doubling every day gets pretty big as the number of days gets larger.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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