SOLUTION: Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is approximated by the equation below. p(x) = 29.92e^-0.2x (x &#

Algebra ->  Linear-equations -> SOLUTION: Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is approximated by the equation below. p(x) = 29.92e^-0.2x (x &#      Log On


   

Question 1073388: Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is approximated by the equation below.
p(x) = 29.92e^-0.2x (x ≥ 0)
If the barometric pressure as measured by a hot-air balloonist is 21 in. of mercury, what is the balloonist's altitude? (Round your answer to two decimal places.)
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Found 2 solutions by jorel1380, Edwin McCravy:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
p(x)=29.92e^-0.2x
21=29.92e^-0.2x
21/29.92=e^-0.2x
e^-0.2x=.70187
ln e^-0.2x=ln .70187
-0.2x ln e=ln .70187
x=ln .70187/-0.2=1.770035376 miles above sea level as the altitude of the balloon. ☺☺☺☺

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
p(x) = 29.92e^-0.2x
The main thing to do here is to look carefully and determine
what x and p(x) stand for.

x stands for balloonist's, altitude in miles above sea level, 
because we see the words

"x mi above sea level".

And since "pressure" begins with the letter "p", since the formula
is for the barometric pressure, we can tell that "p(x)" stands for
pressure (in inches of mercury.

So the formula could be written




So we substitute 21 for p(x), the BAROMETER PRESSURE

matrix%281%2C3%2C%0D%0A%0D%0A%22p%28x%29%22%2C%22%22=%22%22%2C29.92e%5E%28-0.2x%29%29

matrix%281%2C3%2C%0D%0A%0D%0A%2221%22%2C%22%22=%22%22%2C29.92e%5E%28-0.2x%29%29

Divide both sides by 29.92:


matrix%281%2C3%2C%0D%0A%0D%0A21%2F29.92%2C%22%22=%22%22%2Ce%5E%28-0.2x%29%29


Then we take the natural logarithm of both sides:


matrix%281%2C3%2C%0D%0A%0D%0Aln%2821%2F29.92%29%2C%22%22=%22%22%2Cln%28e%5E%28-0.2x%29%29%29

matrix%281%2C3%2C%0D%0A%0D%0Aln%2821%2F29.92%29%2C%22%22=%22%22%2C-0.2x%29

matrix%281%2C3%2C%0D%0A%0D%0A-0.3540047154%2C%22%22=%22%22%2C-0.2x%29

Divide both sides by -0.2

matrix%281%2C3%2C%0D%0A%0D%0A%28-0.3540047154%29%2F%28-0.2%29%2C%22%22=%22%22%2Cx%29

matrix%281%2C3%2C%0D%0A%0D%0A1.770023577%2C%22%22=%22%22%2Cx%29

Rounded to hundredths, the balloonist is 1.77 miles high.

Edwin