The earth’s atmospheric pressure p is often modeled by assuming that the rate dp/dh at which p changes with the altitude h above sea level is proportional to p. Suppose that the pressure at sea level is 1013 millibars (about 14.7 pounds per square inch) and that the pressure at an altitude of 20 km is 90 millibars.

a. Solve the initial value problem

to express p in terms of h. Determine the values of p₀ and k from the given altitude-pressure data.

b. What is the atmospheric pressure at h = 50 km?

c. At what altitude does the pressure equal 900 millibars?

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Differential equation: Initial condition: dp/dh = kp (k a constant) P = Po when h = 0