The following table gives a measurement of atmospheric pressure P, in grams per

Question

The following table gives a measurement of atmospheric pressure P, in grams per square centimeter, at the given altitude A, in kilometers. (**Note: For comparison, 1 km=0.6 mile and 1 g/cm^2 = 2 lbs/ft^2).

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b) Find an exponential model of P as a function of A. Round your parameters to three decimal places.

d) What is the percentage decay rate and explain what this means

e) What is the atmospheric pressure at an altitude of 2 miles? (Hint: See note above-change 2 miles to km)

f) Find the atmospheric pressure of Earth's surface. This is termed standard atmospheric pressure.

g) At what altitude is the atmospheric pressure equal to 25% of standard atmospheric pressure?

** I already drew the graph so I skipped some steps.

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Explanation / Answer

b) Let the altitude A, along the horizontal axis and atmospheric pressure P along the vertical axis.

Then using calculator and plot of the data we get in linear regression plot,

Initial value = a = 1034.651

And growth = b = 0.88732

Hence the model is P(A) = abA = (1034.651)(0.887)A

(d) Here b = 1-r, r is rate of decay

0.887 = 1-r

=> r = 1-0.887 = 0.113

=> 11.3% decay rate

This means that 11.3% of the atmospheric pressure has decayed with altitude

(e) Now 1 km = 0.6 mile

0.6 mile = 1km

2 miles = 2/0.6 km = 20/6 = 3.33 km

P(3.33) = (1034.651)(0.887)3.33 = 694.032 gm./cm2

(f) At A=0

P(0) = (1034.651)(0.887)0 = 1034.651 gm/cm2

(g) 25% of 1034.651 = 258.66275

258.66275 = (1034.651)(0.887)A

=> 0.25 = (0.887)A

=> ln(0.25) = A ln(0.887)

=> -1.386294/-0.119910 = A

=> A = 12 km (approx.)

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