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 #89960 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This looks like exponential growth.<BR>\n" );
document.write( "The formula for exponential growth is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=k%2Ae%5E%28%28alpha%29+t%29 ALIGN=MIDDLE  ALT=\"f%28t%29=k%2Ae%5E%28%28alpha%29+t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We just need to determine <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=k%2Ae%5E%28%28alpha%29%29=5 ALIGN=MIDDLE  ALT=\"f%281%29=k%2Ae%5E%28%28alpha%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=k%2Ae%5E%282%28alpha%29%29=10 ALIGN=MIDDLE  ALT=\"f%282%29=k%2Ae%5E%282%28alpha%29%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282%28alpha%29%29%2Fe%5E%28alpha%29=10%2F5 ALIGN=MIDDLE  ALT=\"e%5E%282%28alpha%29%29%2Fe%5E%28alpha%29=10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28alpha%29=2 ALIGN=MIDDLE  ALT=\"e%5E%28alpha%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28alpha%29=ln%282%29 ALIGN=MIDDLE  ALT=\"%28alpha%29=ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28alpha%29=0.693 ALIGN=MIDDLE  ALT=\"%28alpha%29=0.693\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=k%2Ae%5E%28%28alpha%29%29=5 ALIGN=MIDDLE  ALT=\"f%281%29=k%2Ae%5E%28%28alpha%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Ae%5E%280.693%29=5 ALIGN=MIDDLE  ALT=\"k%2Ae%5E%280.693%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k=5 ALIGN=MIDDLE  ALT=\"2k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2.5 ALIGN=MIDDLE  ALT=\"k=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=2.5%2Ae%5E%280.693t%29 ALIGN=MIDDLE  ALT=\"f%28t%29=2.5%2Ae%5E%280.693t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, what is t so that f(t)>1000000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5%2Ae%5E%280.693t%29%3E1000000 ALIGN=MIDDLE  ALT=\"2.5%2Ae%5E%280.693t%29%3E1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.693t%29%3E400000 ALIGN=MIDDLE  ALT=\"e%5E%280.693t%29%3E400000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.693t%3Eln%28400000%29 ALIGN=MIDDLE  ALT=\"0.693t%3Eln%28400000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.693t%3E12.89922 ALIGN=MIDDLE  ALT=\"0.693t%3E12.89922\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3E18.61 ALIGN=MIDDLE  ALT=\"t%3E18.61\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first time would be the 19th correct question. <BR>\n" );
document.write( "For 19 correct answers, you would win<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2819%29=2.5%2Ae%5E%280.693%2819%29%29 ALIGN=MIDDLE  ALT=\"f%2819%29=2.5%2Ae%5E%280.693%2819%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2819%29=2.5%2Ae%5E%2813.167%29 ALIGN=MIDDLE  ALT=\"f%2819%29=2.5%2Ae%5E%2813.167%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2819%29=1307059.78 ALIGN=MIDDLE  ALT=\"f%2819%29=1307059.78\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The payout would be $1.307,059.78. <BR>\n" );
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