document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=726849>Question 726849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joey saved $2 today. If he doubles the number of dollars he saves each day, how many days, including today, will it take him to save more than $500? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444896 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=444896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a geometric sequence with a factor of 2: 2, 4, 8, 16...<P><BR>\n" );
document.write( "The sum of a geometric series is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%29%2A+%281-r%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%281%29%2A+%281-r%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a(1) is the first term, r is the common factor, and n is the nth term (the number of the term that = the sum).  Set this =  500 and solve for n.  The n needed (the numbered term) will be greater than that n.<P><BR>\n" );
document.write( "a(1) = 2  and r=2.  The desired sum is 500.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500+=+2%2A%281-2%5En%29%2F%281-2%29+ ALIGN=MIDDLE  ALT=\"500+=+2%2A%281-2%5En%29%2F%281-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-500+=+2%281-2%5En%29 ALIGN=MIDDLE  ALT=\"-500+=+2%281-2%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-250+=+1-2%5En ALIGN=MIDDLE  ALT=\"-250+=+1-2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En+=+251 ALIGN=MIDDLE  ALT=\"2%5En+=+251\"   DISABLED_style= \"max-width:90%; height:auto;\" ><P><BR>\n" );
document.write( "Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5En=y ALIGN=MIDDLE  ALT=\"x%5En=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > when log (base x)y = n so log(base 2) 251 = n = approx. 7.97<P><BR>\n" );
document.write( "Therefore the sum of the first 7.97 terms is 500, so the sum exceeds 500 with the 8th term or 8th day.<P><BR>\n" );
document.write( "You could have also solved this by writing out the amount he saved each day, and adding:  2, 4, 8, 16, 32, 64, 128, 256 (the sum is $510, which exceeds $500 on the 8th day.)<BR>\n" );
document.write( "<P>Hope the solution helped.  Sometimes you need more than a solution.  Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );