document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091345>Question 1091345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your friend is saving pennies. She puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, doubling the number of pennies added. How many much money would she have at the end of vacation, if she could keep saving at this rate? Vacation lasts 75 days.\r<BR>\n" );
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document.write( "I would like to know if there is a formula for solving this problem, which I am fairly sure there is. I also have an understanding that the answer is very large. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705725 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "Your friend is saving pennies. She puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, doubling the number of pennies added. How many much money would she have at the end of vacation, if she could keep saving at this rate? Vacation lasts 75 days.<BR>\n" );
document.write( "I would like to know if there is a formula for solving this problem, which I am fairly sure there is. I also have an understanding that the answer is very large.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Indeed, the result is staggering.<BR>\n" );
document.write( "She puts in one penny the first day, 2 pennies the second, 4 pennies the third, ...<BR>\n" );
document.write( "The total sum is thus,<BR>\n" );
document.write( "1, 3, 7, 15, 31, 63, 127, ...<BR>\n" );
document.write( "Which translate to<BR>\n" );
document.write( "2^1-1, 2^2-1, 2^3-1, 2^4-1, 2^5-1, 2^6-1, 2^7-1, ...<BR>\n" );
document.write( "So at the end of the 75th day, the total amount is 2^75-1<BR>\n" );
document.write( "or<BR>\n" );
document.write( "37778931862957161709567 pennies<BR>\n" );
document.write( "or<BR>\n" );
document.write( "377,789,318,629,571,617,095.67 dollars<BR>\n" );
document.write( "or<BR>\n" );
document.write( "three hundred seventy-seven quintillion seven hundred eighty-nine quadrillion three hundred eighteen trillion six hundred twenty-nine billion five hundred seventy-one million six hundred seventeen thousand ninety-five dollars and sixty-seven cents </SPAN>\n" );
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