Solve the problem.

The function defined by
​P(x)=946e−0.0001277x approximates the atmospheric pressure​ (in millibars) at an altitude of x meters. Use P to predict the pressure at 0 meters and 15,000 meters.

1 answer

To predict the pressure at 0 meters, we substitute x = 0 into the equation:

P(0) = 946e^(-0.0001277 * 0)
P(0) = 946e^0
P(0) = 946 * 1
P(0) = 946 millibars

Therefore, the predicted pressure at 0 meters is 946 millibars.

To predict the pressure at 15,000 meters, we substitute x = 15,000 into the equation:

P(15000) = 946e^(-0.0001277 * 15000)
P(15000) = 946e^(-1.9155)
P(15000) ≈ 175.34 millibars

Therefore, the predicted pressure at 15,000 meters is approximately 175.34 millibars.