document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122541>Question 122541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I stuck on this problem and have been for a while. I hope you can help me out!!\r<BR>\n" );
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document.write( "A quiz program gives a prize of $5 for teh first question answered correctly. The contestant's prize winnings are doubled for each question after the first. How many questions would you need to answer to exceed $1,000,000 in total prize money?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89964 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=89964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quiz program gives a prize of $5 for the first question answered correctly. The contestant's prize winnings are doubled for each question after the first. How many questions would you need to answer to exceed $1,000,000 in total prize money?<BR>\n" );
document.write( "5,10,20,40,80,160....<BR>\n" );
document.write( "This is a geometric sequence with r=2 and a=5<BR>\n" );
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document.write( "Sum Formula:<BR>\n" );
document.write( "S(n) = a[1-r^(n)]/[1-r]<BR>\n" );
document.write( "Example: <BR>\n" );
document.write( "S(2) = 5[1-2^(2)]/[1-2] = 5-3/-1 = 15<BR>\n" );
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document.write( "Your Problem:<BR>\n" );
document.write( "1,000,000 = 5[(2^x)-1]/(2-1)<BR>\n" );
document.write( "200,000 = (2^x)-1<BR>\n" );
document.write( "200,001 = 2^x<BR>\n" );
document.write( "Take the log of both sides to get:<BR>\n" );
document.write( "x*log2 = log 200,001<BR>\n" );
document.write( "x = [log200,001]/[log2] <BR>\n" );
document.write( "x = 17.6096<BR>\n" );
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document.write( "When you answer 18 correctly you will be above 1 million in earnings.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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