Modeling Data A meteorologist measures the atmospheric pressure P ( in kilograms per

Chapter 5, Problem 81

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Modeling Data A meteorologist measures the atmospheric pressure P ( in kilograms per square meter) at altitude h ( in kilometers). The data are shown below. rp Linear and Quadratic Approximations In Exercises 8.^ and 84, use a graphing utility to graph the function. Then graph l\(x) =/((!) +,/'(0)(.v - (I) and PAx) =/(()) +/'(OH.v - 0) + \j"m{x - ())- in the same viewing window. Compare the \ahies of/, /',, and P, and their first derivatives at x = 0. 83. /(.v) = '/= 84. fix) -.-/:: h 5 10 15 20 P 10,332 5.583 2376 1240 517 rp 85. Finding a Pattern Use a graphing uliliU to compare the graph of the function y = c' with Ihe graphs of each ot the followins; functions. ^ (a) Use a graphing utilit\ to ploi the points (/i. In /'). Use the regression capabilities of the graphing utilit\ lo find a linear model for the revised data points (b) The line in part (a) has the form In F = tih + />. Write the equation in exponential form. (c) Use a graphing ulilil\ to plot the original tlala and graph the exponential model in part (bl. (d) Find the rate of change of the piessuie when h = 5 and h = 18.