document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469372>Question 469372</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 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( "The \"learning curve\" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by the following formula.<BR>\n" );
document.write( "t = - 62.5 ln\(1-N/80\)\r<BR>\n" );
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document.write( "(a) According to this formula, what is the maximum number of words per minute?\r<BR>\n" );
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document.write( "(b) Solve for N.<BR>\n" );
document.write( "N = \r<BR>\n" );
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document.write( "The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)<BR>\n" );
document.write( "P = 14.7 e**(-0.21 a)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322039 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We want the least positive integer such that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+%3E+15+%2A+10%5E22+=+1.5+%2A+10%5E23 ALIGN=MIDDLE  ALT=\"2%5Ex+%3E+15+%2A+10%5E22+=+1.5+%2A+10%5E23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "taking common logs of both sides, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog2+%3E+log1.5+%2B+log+10%5E23+=+log1.5+%2B+23 ALIGN=MIDDLE  ALT=\"x%2Alog2+%3E+log1.5+%2B+log+10%5E23+=+log1.5+%2B+23\"   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=+x+%3E+%28log1.5+%2B+23%29%2Flog2+=+76.9893 ALIGN=MIDDLE  ALT=\"+x+%3E+%28log1.5+%2B+23%29%2Flog2+=+76.9893\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> let x = 77.  Hence after the 77th minute. </SPAN>\n" );
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