document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=574553>Question 574553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Heeding the advice to “Go west, young man,” Harold and Horace greedy set out for Las Vegas to make their fortunes. Luck was with the greedy brothers, for each doubled his money every hour. Harold, who began with $20, gambled for 20 hours and then sent his fortune home. The next day, Horace began with $40 and gambled until his fortune matched his brother’s. For how many hours did Horace Greedy gamble that day. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369190 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Harold Greedy started with $20. After $1 hour, he had $40. It took him 19 more hours to go from $40 to the amount/fortune he wanted. I'll call it X, but I do not have to calculate it.<BR>\n" );
document.write( "Horace, started with $40, and increased his fortune at the same rate as his brother had done.<BR>\n" );
document.write( "So he got from $40 to X in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2819%29 ALIGN=MIDDLE  ALT=\"highlight%2819%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours, just like his brother had done before.<BR>\n" );
document.write( "My question is, was the official solution to the problem unnecessarily more complicated than that?<BR>\n" );
document.write( "JUST FOR FUN (and to apply a little of the stuff you're learning in class)<BR>\n" );
document.write( "The brothers' fortunes were increasing in geometric sequence (or geometric progression, depending on book/teacher/country).<BR>\n" );
document.write( "After n hours Harold had<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A2%5En ALIGN=MIDDLE  ALT=\"20%2A2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After 20 hours he had<BR>\n" );
document.write( "X=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A2%5E20 ALIGN=MIDDLE  ALT=\"20%2A2%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I still do not have to calculate it<BR>\n" );
document.write( "Horace, starting with $40, would have<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2A2%5Et ALIGN=MIDDLE  ALT=\"40%2A2%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > after t hours<BR>\n" );
document.write( "When Horace's fortune matched his brother's X=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A2%5E20 ALIGN=MIDDLE  ALT=\"20%2A2%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we would have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2A2%5Et=20%2A2%5E20 ALIGN=MIDDLE  ALT=\"40%2A2%5Et=20%2A2%5E20\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Et=20%2A2%5E20%2F40 ALIGN=MIDDLE  ALT=\"2%5Et=20%2A2%5E20%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Et=2%5E20%2F2 ALIGN=MIDDLE  ALT=\"2%5Et=2%5E20%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Et=2%5E%2820-1%29 ALIGN=MIDDLE  ALT=\"2%5Et=2%5E%2820-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Et=2%5E19 ALIGN=MIDDLE  ALT=\"2%5Et=2%5E19\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C+2%5Et%29=log%282%2C+2%5E19%29 ALIGN=MIDDLE  ALT=\"log%282%2C+2%5Et%29=log%282%2C+2%5E19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=19%29 ALIGN=MIDDLE  ALT=\"highlight%28t=19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK. I'm curious. I'll calculate it after all.<BR>\n" );
document.write( "X=$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A1048576 ALIGN=MIDDLE  ALT=\"20%2A1048576\"   DISABLED_style= \"max-width:90%; height:auto;\" >=$20,971,520 </SPAN>\n" );
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