Question

Atmospheric pressure, measured in pounds per square inch (\text{psi})(psi)left parenthesis, p, s, i, right parenthesis is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, ppp, exerted on an airplane flying at an altitude of aaa miles above sea level can be approximated by the model shown above. What is the best interpretation of {0.8^a}0.8 a 0, point, 8, start superscript, a, end superscript in this equation?

Answer 1

Circle in thexyxyx, y‑plane has the equation(x+92)^2+(y+54)^2=73(x+92)2+(y+54)2=73left parenthesis, x, plus, 92, right parenthesis, start superscript, 2, end superscript, plus, left parenthesis, y, plus, 54, right parenthesis, start superscript, 2, end superscript, equals, 73. What is the length of the diameter of the circle?

Answer 2

Answer:

For each mile that the altitude increases, the atmospheric pressure decreases 20%.

Explanation:

Given the formula:

p = 14.63*0.8^a

where p is the atmospheric pressure in psi, and a is the altitude above the sea in miles, the 0.8^a means that for each mile that the altitude increases, the atmospheric pressure decreases a 20% respect the pressure in the mile below. Fro example:

a (in miles)    p (in psi)

0                   14.63*0.8^0 = 14.63 psi                

1                    14.63*0.8^1 = 14.63*0.8            (20% less than a mile before)  

2                   14.63*0.8^2 = 14.63*0.8*0.8    (20% less than a mile before)