The atmospheric pressure decreases with increasing altitude. At sea level, the average
Chapter 4, Problem 34(choose chapter or problem)
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 ±5 percent. The ordered pairs (h, p) give the pressures p (in atmospheres) for various altitudes h (in kilometers). (Spreadsheet at LarsonPrecalculus.com)
(0, 1), (10, 0.25), (20, 0.06), (5, 0.55), (15, 0.12), (25, 0.02)
(a) Use the regression feature of a graphing utility to attempt to find the logarithmic model p = a + b ln h for the data. Explain why the result is an error message.
(b) Use the regression feature of the graphing utility to find the logarithmic model h = a + b ln p for the data.
(c) Use the graphing utility to plot the data and graph the logarithmic model in the same viewing window.
(d) Use the model to estimate the altitude at which the pressure is 0.75 atmosphere.
(e) Use the graph in part (c) to estimate the pressure at an altitude of 13 kilometers.
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