SOLUTION: The altitude of an aircraft, h, in miles, is given by h= - (100/9)log p/b where P = the outside pressure and B = the atmospheric pressure at sea level. Let B = 31 inches of mer

Question 713101: The altitude of an aircraft, h, in miles, is given by
h= - (100/9)log p/b
where P = the outside pressure and B = the atmospheric pressure at sea level. Let B = 31 inches of mercury. What is the outside air pressure at a height of 2.7 miles? Round your answer to the nearest tenth.

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Substituting in the values given for b and h we get:

And now we solve for p. First we'll isolate the log. Multiplying both sides by -9/100:

Next we rewrite the equation in exponential form. In general is equivalent to . Using this pattern (and the fact that the base of "log" is 10) on our equation we get:

Next we multiply both sides by 31:

This is an exact expression for the solution. I'll leave it up to you to use your calculator to find the decimal. (Just be sure to raise 10 to the -.243 power before you multiply by 31.)

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