SOLUTION: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e^-0.21x , where x is the number of miles above sea level. To the nearest foot, how high is t

Question 1192255: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e^-0.21x , where x is the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 8.325 pounds per square inch? Hint: There are 5280 feet in a mile.
Can you please explain each step in writing? Example

Apply the inverse property of logs.
=m+n
Substitute for m and n
=logb(M)+logb(N)
Thank you.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

psi = pounds per square inch

We're given a pressure of 8.325 psi.
This is the value of P we'll plug in to find x.

Replace P with 8.325

Divide both sides by 14.7

Simplify. The left hand side is approximate.

Apply natural logs to both sides

The last step was done so we can pull down the exponent according to the rule that Ln(x^y) = y*Ln(x)

Then we use the rule that Ln(e) = 1.

Simplify

Flip the sides of the equation.

Divide both sides by -0.21 to isolate x entirely.

Simplify. This value is approximate.

This x value is in miles, and its the number of miles above sea level.

To convert to feet, we multiply by 5280 since 1 mile = 5280 ft.

2.707541*5280 = 14,295.81648

That rounds to 14,296 when rounding to the nearest foot.

Answer: 14,296 feet

RELATED QUESTIONS
The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, (answered by ankor@dixie-net.com)

The atmospheric pressure p in pounds per square inch (psi) is given by P=14.7e^0.21a... (answered by macston)

The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7... (answered by kevwill)

The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7... (answered by stanbon)

The average atmospheric pressure P is pounds per square inch is P = 14.7e-0.21x where x... (answered by josmiceli)

The function p(x)=14.7e^-0.21x models the average atmospheric pressure, P(x), in pounds... (answered by josgarithmetic)

I need help with this problem! Air pressure at sea level is approximately 14.7 pounds... (answered by rothauserc)

The equation P(a) = 14.7e^(-0.2a), where a is the altitude above sea level in miles,... (answered by harpazo)