The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
P = 14.7 e**(-0.21 a)
ft
Since you have the formula, what's the holdup? Plug in your values.
Hint: use logs -- ln(e^x) = x
ln P = ln 14.7 - .21a
2.3
To find the altitude of the city when given the atmospheric pressure, we can use the given formula:
P = 14.7 * e^(-0.21a)
In this formula, P represents the atmospheric pressure in psi, and a represents the altitude in miles.
Given that the city has an atmospheric pressure of 13.25 psi, we can substitute this value into the formula:
13.5 = 14.7 * e^(-0.21a)
To solve for the altitude 'a', we can rearrange the equation algebraically:
e^(-0.21a) = (13.25 / 14.7)
Taking the natural logarithm (ln) of both sides of the equation will help us isolate 'a':
ln(e^(-0.21a)) = ln(13.25 / 14.7)
Simplifying further:
-0.21a = ln(13.25 / 14.7)
Dividing both sides by -0.21 to solve for 'a':
a = ln(13.25 / 14.7) / -0.21
Using a calculator to evaluate the right side of the equation approximately gives:
a ≈ ln(0.8993) / -0.21
Now, let's calculate the value of 'a':
a ≈ -2.39
Since altitude cannot be negative, we can conclude that there was an error in the given information or calculation, or the formula may not accurately represent the relationship between atmospheric pressure and altitude. Please double-check the provided data or formula to find the correct altitude value.