The air pressure p (h) (in lb/ in²) at an altitude of h feet above sea level may be approximated by the formula $p ( h ) = 14.7 e ^ { - 0.0000385 h }$ At approximately what altitude h is the air pressure 9 lb/ in² ? A) 12,743 ft B) 1,274 ft C) 17,123 ft D) 5,534 ft E) 553 ft

Question

Quizplus · Accepted Answer

To find the altitude where the air pressure is 9 lb/in², solve the equation $9 = 14.7 e^{-0.0000385h}$. Dividing both sides by 14.7 gives $e^{-0.0000385h} = \frac{9}{14.7}$. Taking the natural logarithm of both sides and solving for h gives $h \approx 12,743$ ft.

The Air Pressure P (H) (In Lb/ In 2 ) p(h)=14.7e−0.0000385hp ( h ) = 14.7 e ^ { - 0.0000385 h }p(h)=14.7e−0.0000385h

The Air Pressure P (H) (In Lb/ In²) $p ( h ) = 14.7 e ^ { - 0.0000385 h }$