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 12.17 psi, what is its altitude?
you are solving
12.17 = 14.7 e^(-.21a)
.827891156 = e^(-.21a)
ln (.827891156) = -.21a lne
-.21a = -.188873...
a = appr .8994 miles or appr 4750 ft to the nearest ten feet.
To find the altitude of the city given the atmospheric pressure, we need to rearrange the formula and solve for a.
The formula given is: P = 14.7 e^(-0.21a)
Step 1: Substitute the given atmospheric pressure: P = 12.17 psi
Step 2: Rearrange the formula: 12.17 = 14.7 e^(-0.21a)
Step 3: Divide both sides of the equation by 14.7: 12.17/14.7 = e^(-0.21a)
Step 4: Take the natural logarithm of both sides to remove the exponential: ln(12.17/14.7) = -0.21a
Step 5: Divide both sides of the equation by -0.21: ln(12.17/14.7) / -0.21 = a
Step 6: Use a calculator to evaluate the left side of the equation: a ≈ 6.25 miles
Therefore, the altitude of the city is approximately 6.25 miles above sea level.