The atmospheric pressure $P(h)$ (in pounds per square inch) at a height $h$ (in miles) above sea level on Earth satisfies a differential equation $P' = -kP$ for some positive constant $k$.

(a) Measurements with a barometer show that $P(0) = 0.5$ and $P(7) = 0.1$. What is the decay constant $k$?
(b) Determine the atmospheric pressure 15 miles above sea level.

(a) $k =$
(b) $P(15)=$