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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (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.

P+=+14.7e%5E%28-0.21x%29

8.325+=+14.7e%5E%28-0.21x%29 Replace P with 8.325

8.325%2F14.7+=+e%5E%28-0.21x%29 Divide both sides by 14.7

0.566327+=+e%5E%28-0.21x%29 Simplify. The left hand side is approximate.

ln%280.566327%29+=+ln%28e%5E%28-0.21x%29%29 Apply natural logs to both sides

ln%280.566327%29+=+-0.21x%2Aln%28e%29 The last step was done so we can pull down the exponent according to the rule that Ln(x^y) = y*Ln(x)

ln%280.566327%29+=+-0.21x%2A1 Then we use the rule that Ln(e) = 1.

ln%280.566327%29+=+-0.21x Simplify

-0.21x+=+ln%280.566327%29 Flip the sides of the equation.

x+=+%28ln%280.566327%29%29%2F%28-0.21%29 Divide both sides by -0.21 to isolate x entirely.

x+=+2.707541 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