A meteorologist measures the atmospheric pressure P (in kilograms per square meter) at altitude h (in kilometers). The data are shown below. Use the regression capabilities of the Graphing utility to find a linear model for the revised data points obtained by plotting the points $( h , \ln P )$ $\begin{array}{|c|c|c|c|c|c|}
\hline h & 0 & 5 & 10 & 15 & 20 \
\hline p & 28,085 & 15169 & 6,458 & 3,371 & 1,405 \
\hline
\end{array}$

A) $\ln P = - 0.1499 h + 10.3018$
B) $\ln P = - 0.1944 h - 14.3601$
C) $\ln P = 0.1944 h + 10.3601$
D) $\ln P = - 0.1499 h - 14.3016$
E) $\ln P = - 0.1499 h - 10.3018$

Question

A meteorologist measures the atmospheric pressure P (in kilograms per square meter) at altitude h (in kilometers). The data are shown below. Use the regression capabilities of the Graphing utility to find a linear model for the revised data points obtained by plotting the points $( h , \ln P )$ $\begin{array}{|c|c|c|c|c|c|}
\hline h & 0 & 5 & 10 & 15 & 20 \
\hline p & 28,085 & 15169 & 6,458 & 3,371 & 1,405 \
\hline
\end{array}$

A) $\ln P = - 0.1499 h + 10.3018$
B) $\ln P = - 0.1944 h - 14.3601$
C) $\ln P = 0.1944 h + 10.3601$
D) $\ln P = - 0.1499 h - 14.3016$
E) $\ln P = - 0.1499 h - 10.3018$

Quizplus · Accepted Answer

To find a linear model for the revised data points obtained by plotting the points $$(h, \ln P)$$ we need to first take the natural logarithm of the given atmospheric pressure data. Then, we plot the points $$(h, \ln P)$$ and use the regression capabilities of the graphing utility to find a linear model that best fits the data.

Taking the natural logarithm of the atmospheric pressure data, we get:

\begin{align*}
\ln 28085 \approx 10.2425 \
\ln 15169 \approx 9.6252 \
\ln 6458 \approx 8.7742 \
\ln 3371 \approx 8.1237 \
\ln 1405 \approx 7.2473 \
\end{align*}

Plotting these points and performing a linear regression with the calculator gives the equation:

$$\ln P = -0.1499 h + 10.3018$$

Therefore, the best choice is $\boxed{	extbf{(A)}}.$

A Meteorologist Measures the Atmospheric Pressure P (In Kilograms Per (h,ln⁡P)( h , \ln P )(h,lnP)

A Meteorologist Measures the Atmospheric Pressure P (In Kilograms Per $( h , \ln P )$