The atmospheric pressure P, in pounds per square inch, at x miles above sea level is given approximately by P=22.2e−0.31x

Question

At what height will the atmospheric pressure be one-fifth the sea level pressure?

Answer 1

P = 22.2e^=0.31x

Pressure at sea level = 22.2e⁰ = 22.2

22.2/5 = 22.2e^-0.31x

0.2 = e^-0.31x

-0.31x = ln(0.2)

x = ln(0.2) / (-0.31)

Answer 2

P_x / P₀ = 1 / 5

5 P_x = P₀

5(22.2e - 0.31x) = 22.2e - 0.31(0)

Can you solve for x and answer?