The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressure is approximately $1.03323$ kilograms per square centimeter, and this pressure is called one atmosphere. Variations in weather conditions cause changes in the atmospheric pressure of up to $\pm 5$ percent. The table below shows the pressures $p$ (in atmospheres) for various altitudes $h$ (in kilometers). Use the regression feature of a graphing utility to find the logarithmic model $h = a + b \ln p$ for the data. Use the model to estimate the altitude at which the pressure is $0.28$ atmosphere. Round your answer to two decimal places.

A) 4.54 kilometers
B) 10.88 kilometers
C) 7.44 kilometers
D) 9.07 kilometers
E) 8.34 Kilometers

Question

The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressure is approximately $1.03323$ kilograms per square centimeter, and this pressure is called one atmosphere. Variations in weather conditions cause changes in the atmospheric pressure of up to $\pm 5$ percent. The table below shows the pressures $p$ (in atmospheres) for various altitudes $h$ (in kilometers). Use the regression feature of a graphing utility to find the logarithmic model $h = a + b \ln p$ for the data. Use the model to estimate the altitude at which the pressure is $0.28$ atmosphere. Round your answer to two decimal places.

A) 4.54 kilometers 
B) 10.88 kilometers 
C) 7.44 kilometers 
D) 9.07 kilometers 
E) 8.34 Kilometers

Quizplus · Accepted Answer

Using a regression feature of a graphing calculator, we get the equation $h \approx -8.36429\ln(p)-5.15635$. Solving for $p=0.28$, we get $h \approx 9.07$ kilometers. Therefore, the answer is $\boxed{	extbf{(D)}}$.

The Atmospheric Pressure Decreases with Increasing Altitude 1.033231.033231.03323 Kilograms Per Square Centimeter, and This Pressure Is Called One

The Atmospheric Pressure Decreases with Increasing Altitude $1.03323$ Kilograms Per Square Centimeter, and This Pressure Is Called One