The atmospheric pressure P in pounds per square inch (psi) is given by
P = 14.7 e^−0.21 a
where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 11.35 psi, what is its altitude?
Thought this looked familar.
Just change the numbers a bit
http://www.jiskha.com/display.cgi?id=1384227123
answer is 6503 miles?
I have no clue how you got your answer, but did you think about the validity of your answer?
A city 6503 miles high would put it in a pretty high orbit.
The space station is only about 230 miles high.
11.35 = 14.7 e^(-.21a)
.7721088.. = e^(-.21a)
-.21a ln e = ln .7721088..
a = ln .7721088.. / -.21 , remember ln e = 1
=1.2315 miles or appr 6500 ft
To find the altitude of a city with a given atmospheric pressure, we can rearrange the formula and solve for 'a':
P = 14.7 e^(-0.21a)
We are given that the atmospheric pressure P is 11.35 psi. Substituting this value into the equation, we get:
11.35 = 14.7 e^(-0.21a)
To solve for 'a', we need to isolate it on one side of the equation.
First, let's divide both sides of the equation by 14.7:
11.35/14.7 = e^(-0.21a)
Now, we can take the natural logarithm (ln) of both sides of the equation to eliminate the exponential term:
ln(11.35/14.7) = -0.21a
Next, we divide both sides of the equation by -0.21 to solve for 'a':
a = ln(11.35/14.7) / -0.21
Calculating this expression, we find:
a ≈ 7.468 miles
Therefore, the altitude of the city is approximately 7.468 miles above sea level.