Question

atmospheric pressure in pounds per square inch is represented by the formula , where 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 pounds per square inch? hint: there are 5280 feet in a mile.

Answer 1

The peak of a mountain with an atmospheric pressure of 8.762 pounds per square inch is 13,010 feet high.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

`f(x)=a(b)^x`

Where:

• a represents the initial value or y-intercept.
• x represents x-variable.
• b represents the rate of change or common ratio.

By substituting the atmospheric pressure at the peak of a mountain into the exponential function, we have the following;

`P=14.7e^(-0.21x)\\\\8.762=14.7e^(-0.21x)\\\\(8.762)/(14.7) =e^(-0.21x)\\\\ln((8.762)/(14.7)) =ln(e^(-0.21x))\\\\ln(0.59605442176870748299319727891156)=-0.21x\\\\-0.51742330439=-0.21x\\\\x=(0.51742330439)/(0.21)`

x = 2.4639204970952380952380952380952 miles above sea level.

Next, we would convert the height in miles to feet as follows;

x = 2.4639204970952380952380952380952 × 5280

x = 13009.50 ≈ 13,010 feet.

Complete Question:

Atmospheric pressure in pounds per square inch is represented by the formula
`P=14.7e^(-0.21x)`, where 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 8.762 pounds per square inch? (hint: there are 5280 feet in a mile.)