document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192255>Question 1192255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e^-0.21x , where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.325 pounds per square inch? Hint: There are 5280 feet in a mile.\r<BR>\n" );
document.write( "\n" );
document.write( "Can you please explain each step in writing? Example <BR>\n" );
document.write( "  <BR>\n" );
document.write( "                         <BR>\n" );
document.write( "Apply the inverse property of logs.<BR>\n" );
document.write( "=m+n\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute for m and n<BR>\n" );
document.write( "=logb(M)+logb(N)             \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824166 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "psi = pounds per square inch\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're given a pressure of 8.325 psi.<BR>\n" );
document.write( "This is the value of P we'll plug in to find x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+14.7e%5E%28-0.21x%29 ALIGN=MIDDLE  ALT=\"P+=+14.7e%5E%28-0.21x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.325+=+14.7e%5E%28-0.21x%29 ALIGN=MIDDLE  ALT=\"8.325+=+14.7e%5E%28-0.21x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace P with 8.325\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.325%2F14.7+=+e%5E%28-0.21x%29 ALIGN=MIDDLE  ALT=\"8.325%2F14.7+=+e%5E%28-0.21x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 14.7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.566327+=+e%5E%28-0.21x%29 ALIGN=MIDDLE  ALT=\"0.566327+=+e%5E%28-0.21x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. The left hand side is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.566327%29+=+ln%28e%5E%28-0.21x%29%29 ALIGN=MIDDLE  ALT=\"ln%280.566327%29+=+ln%28e%5E%28-0.21x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply natural logs to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.566327%29+=+-0.21x%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%280.566327%29+=+-0.21x%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The last step was done so we can pull down the exponent according to the rule that Ln(x^y) = y*Ln(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.566327%29+=+-0.21x%2A1 ALIGN=MIDDLE  ALT=\"ln%280.566327%29+=+-0.21x%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Then we use the rule that Ln(e) = 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.566327%29+=+-0.21x ALIGN=MIDDLE  ALT=\"ln%280.566327%29+=+-0.21x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.21x+=+ln%280.566327%29 ALIGN=MIDDLE  ALT=\"-0.21x+=+ln%280.566327%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the sides of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28ln%280.566327%29%29%2F%28-0.21%29 ALIGN=MIDDLE  ALT=\"x+=+%28ln%280.566327%29%29%2F%28-0.21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -0.21 to isolate x entirely.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.707541 ALIGN=MIDDLE  ALT=\"x+=+2.707541\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. This value is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This x value is in miles, and its the number of miles above sea level.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To convert to feet, we multiply by 5280 since 1 mile = 5280 ft.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.707541*5280 = 14,295.81648\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That rounds to 14,296 when rounding to the nearest foot.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>14,296 feet</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );