The atmospheric pressure decreases with increasing altitude. At sea level, the average air pressure is one atmosphere (1.033227 kilograms per square centimeter). The table shows the pressures p (in atmospheres) at selected altitudes h (in kilometers).

(a) Use a graphing utility to find a model of the form p = a + b ln h for the data. Explain why the result is an error message.(b) Use a graphing utility to find the logarithmic model h = a + b ln p for the data.(c) Use a graphing utility to plot the data and graph the model from part (b).(d) Use the model to estimate the altitude when p = 0.75.(e) Use the model to estimate the pressure when h = 13.(f) Use the model to find the rates of change of pressure when h = 5 and h = 20. Interpret the results.

Transcribed Image Text:

h0 5 10 15 1 0.55 20 0.25 0.12 0.06 P 25 0.02