document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237233>Question 237233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Atmospheric pressure P at an elevation of a feet above sea level is given by <BR>\n" );
document.write( "P=P0e-0.00004a<BR>\n" );
document.write( "Where P0 is the pressure at sea level,which is approximately 29.9 in inches of mercury(Hg).<BR>\n" );
document.write( "Explain how a barometer, or some other device for measuring atmospheric pressure , can be used to find the height of a skyscraper.<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 #174477 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation would be:\r<BR>\n" );
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document.write( "P[a] =P[0] * e^(-0.00004*a)\r<BR>\n" );
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document.write( "^ means raise to the power of\r<BR>\n" );
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document.write( "a appears to be altitude<BR>\n" );
document.write( "p[0] = 29.9 inches of mercury\r<BR>\n" );
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document.write( "p[a] would be the inches of mercury at an altitude of \"a\" feet.\r<BR>\n" );
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document.write( "since p[0] = 29.9 inches of mercury, we can replace p[0] in the equation with 29.9\r<BR>\n" );
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document.write( "assuming a = 0, then this equation would become:\r<BR>\n" );
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document.write( "p[0] = 29.9 * e^(-.00004*0) \r<BR>\n" );
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document.write( "this would become:\r<BR>\n" );
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document.write( "p[0] = 29.9 * e^0 which would become p[0] = 29.9 which would be correct since we would be at sea level.\r<BR>\n" );
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document.write( "if you were on a structure that was 1000 feet high, then this equation would become:\r<BR>\n" );
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document.write( "p[1000] = 29.9 * e^(-.00004*1000) which would become:\r<BR>\n" );
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document.write( "p[1000] = 29.9 * .960789439 which would become:\r<BR>\n" );
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document.write( "p[1000] = 28.72760423\r<BR>\n" );
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document.write( "If you want to measure the height of a building, all you have to do is go to the top of the building and measure the atmospheric pressure.\r<BR>\n" );
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document.write( "Once you have that, you can plug the value into the equation and solve for the height.\r<BR>\n" );
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document.write( "As an example:\r<BR>\n" );
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document.write( "Assume you go to the top of the building and you measure the atmospheric pressure to get:\r<BR>\n" );
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document.write( "atmospheric pressure at top of building = 27 inches of mercury.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "p[a] = 29.9 * e^(-.00004*a)\r<BR>\n" );
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document.write( "Since you already know p[a], then you plug it into the equation to get:\r<BR>\n" );
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document.write( "27 = 29.9 * e^(-.00004*a)\r<BR>\n" );
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document.write( "divide both sides of this equation by 29.9 to get:\r<BR>\n" );
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document.write( "27/29.9 = e^(-.00004*a) which becomes:\r<BR>\n" );
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document.write( ".903010033 = e^(-.00004*a)\r<BR>\n" );
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document.write( "take the natural log of both sides of this equation to get:\r<BR>\n" );
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document.write( "ln(.903010033) = ln(e^(-.00004*a))\r<BR>\n" );
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document.write( "using the laws of logarithms, this equation becomes:\r<BR>\n" );
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document.write( "ln(.903010033) = ln(e) * (-.00004*a)\r<BR>\n" );
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document.write( "since ln(e) = 1, this equation becomes:\r<BR>\n" );
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document.write( "ln(.903010033) = -.00004*a\r<BR>\n" );
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document.write( "divide both sides of this equation by (-.00004) to get:\r<BR>\n" );
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document.write( "ln(.903010033)/(-.00004) = a\r<BR>\n" );
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document.write( "solve for a to get:\r<BR>\n" );
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document.write( "a = 2550.54036 feet.\r<BR>\n" );
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document.write( "the building would be approximately 2550 feet in height.\r<BR>\n" );
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document.write( "that's a very tall building, but that's only because I chose 27 inches of mercury at random without really knowing how high that would be.\r<BR>\n" );
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document.write( "in reality your measurement of atmospheric pressure would probably be around 28 or higher.\r<BR>\n" );
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