A meteorologist measures the atmospheric pressure (in kilograms per square meter

Question

A meteorologist measures the atmospheric pressure (in kilograms per square meter) at altitude h (in kilometers). The data are shown below Altitude, h 0 10 15 20 Pressure, P10,332 5583 2376 1240 517 (a) Use the regression capabilities of a graphing utility to find a least squares regression line for the points (h, In P). (Round your coefficients to four decimal places.) In(P)--0. 1944h-7.3601 | X (b) The result in part (a) is an equation of the form in P = ah + b. Write this logarithmic form in exponential form. (Round your coefficients to four decimal places.) (c) Use a graphing utility to plot the original data and graph the exponential model in part (b). If your graphing utility can fit logarithmic models to data, use it to verify the result in part (b). 10000 10000 5000 10 15 20 10 15 20 10000 10000 5000 5000 10 15 20 10 15 20

Explanation / Answer

Go to xuru.org --> regression tools ---> linear regression

First we find the ln of all those values of P

And enter these points :
(0 , 9.2430011542157311)
(5 , 8.6274815453103604)
(10 , 7.7731736804825355)
(15 , 7.1228666585990825)
(20 , 6.2480428745084291)

And hit "CAlculate"

I get :
y = -0.1499x + 9.3018

So, the ans is :
ln(P) = -0.1499h + 9.3018 ------> ANS

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Exp form :
P = e^(-0.1499h + 9.3018)

P = e^(-0.1499h)*e^(9.3018)

P = 10957.7254e^(-0.1499h) ------> ANS

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The graph is

BOTTOM RIGHT

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