document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=559457>Question 559457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about One hundred and fifty sextillion gallons (that is a fifteen followed by twenty-two zeros). If Hephaetus' machine pours out 2 gallon in the first minute and then doubles its output each minute, find in<BR>\n" );
document.write( "which minute would this hypothetical machine pour out a single quantity of water that would be enough to fill Zeus' chalice with water?\r<BR>\n" );
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document.write( "put in minutes<BR>\n" );
document.write( "i only get the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A10%5E22 ALIGN=MIDDLE  ALT=\"15%2A10%5E22\"   DISABLED_style= \"max-width:90%; height:auto;\" > I dont know how to set this problem up to solve as my logrithmic knowledge is minor\r<BR>\n" );
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document.write( "Help will be greatly appreciated </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #363435 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=363435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about One hundred and fifty sextillion gallons (that is a fifteen followed by twenty-two zeros). If Hephaetus' machine pours out 2 gallon in the first minute and then doubles its output each minute, find in<BR>\n" );
document.write( "which minute would this hypothetical machine pour out a single quantity of water that would be enough to fill Zeus' chalice with water?<BR>\n" );
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document.write( "First, consider how much water is added to the chalice each minute.<BR>\n" );
document.write( "During the 1st minute, there are 2 gallons added to the chalice<BR>\n" );
document.write( "During the 2nd minute, there are 4 gallons added<BR>\n" );
document.write( "During the 3rd minute, there are 8 gallons added, etc.<BR>\n" );
document.write( "The number of gallons added for each successive minute consists of a geometric sequence: 2,4,8,16,...<BR>\n" );
document.write( "To determine how long it takes to fill the chalice, we need to sum this sequence<BR>\n" );
document.write( "The sum of a geometric sequence with common ratio r is:<BR>\n" );
document.write( "S(n) = a(1-r^n)/(1-r) where a = the first term<BR>\n" );
document.write( "In this case a = 2 and r = 2:<BR>\n" );
document.write( "S(n) = 2(1-2^n)/(1-2) = 2(2^n - 1) = 15*10^22<BR>\n" );
document.write( "We need to solve for n:<BR>\n" );
document.write( "2^n - 1 = 7.5E22 [Scientific notation]<BR>\n" );
document.write( "2^n = 7.5E22 + 1<BR>\n" );
document.write( "Take the logarithm of both sides:<BR>\n" );
document.write( "n*log(2) = log(7.5E22 + 1) <BR>\n" );
document.write( "n = 22.875/0.301 = 75.997 min., so the chalice gets filled in the 76th minute<BR>\n" );
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