document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73431>Question 73431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IF YOU EARN $1 THE FIRST DAY OF WORK AND YOU SALARY IS DOUBLE EVERY DA1 (I.E. 1,2,4,8,16,32)HOW MUCH WILL YOU HAVE EARNED AFTER 30 DAYS? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52559 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a geometric progression.  Every term is double the preceding term.  Most beginning<BR>\n" );
document.write( "math books will derive and show you the equation for the sum of the terms in a geometric<BR>\n" );
document.write( "progression.<BR>\n" );
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document.write( "This equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28a%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S+=+%28a%281-r%5En%29%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where the variables are defined as:<BR>\n" );
document.write( "S = the sum of the terms in the given progression<BR>\n" );
document.write( "a = the first term.  In this problem the first term is 1<BR>\n" );
document.write( "r = the common ratio.  In this problem the common ratio is 2 (terms are doubled) <BR>\n" );
document.write( "n = the number of terms.  In this problem n = 30<BR>\n" );
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document.write( "Let's now just substitute numbers for this problem into the equation for the sum to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%281%281-2%5E30%29%29%2F%281-2%29 ALIGN=MIDDLE  ALT=\"S+=+%281%281-2%5E30%29%29%2F%281-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can eliminate the multiplier 1 in the numerator, and the denominator becomes -1.<BR>\n" );
document.write( "With these two changes the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%281-2%5E30%29%2F%28-1%29+=+-%281-2%5E30%29+ ALIGN=MIDDLE  ALT=\"S+=+%281-2%5E30%29%2F%28-1%29+=+-%281-2%5E30%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A calculator will tell you that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E30+=+1073741824 ALIGN=MIDDLE  ALT=\"2%5E30+=+1073741824\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting this results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+-%281-1073741824%29+=+-%28-1073741823%29+=+1073741823 ALIGN=MIDDLE  ALT=\"S+=+-%281-1073741824%29+=+-%28-1073741823%29+=+1073741823\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars<BR>\n" );
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document.write( "Not a bad deal. Start with a dollar on day 1 and 30 days later be worth $1,073,741,823.<BR>\n" );
document.write( "A billionaire in just a month.<BR>\n" );
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document.write( "Hope this helps you see how to work the problem.<BR>\n" );
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