At an altitude of $h$ feet above sea level, the air pressure, $P$, in inches of mercury (in Hg), is given by $$P = 30 e^{-3.23 \times 10^{-5}h}.$$ An unpressurized seaplane takes off at an angle of $20^{\circ}$ to the horizontal and a speed of $110$ mph. What is the rate of change of pressure in the plane with respect to time at take-off, in inches of mercury per second?

rate of change =