A meteorologist measures the atmospheric pressure $P($in kilograms per square meter$)$ at altitude $h($in kilometers$).$ The data are shown below.

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$\backslash$table$[[$Altitude$,h,0,5,10,15,20],[$Pressure$,P,10,322,5,593,2,386,1,250,507]]$

$($a$)$ Use the regression capabilities of a graphing utility to find the least squares regression line for the points $(h,ln(P)).($Round your numerical values to four decimal places.$)$

$ln(P)=$

$($b$)$ The result in part $($a$)$ is an equation of the form $ln(P)=ah+b.$ Write this logarithmic form in exponential form. $($Round your numerical values to four decimal places.$)$

$P=$

$($c$)$ Use a graphing utility to plot the original data and graph the exponential model in part $($b$).($Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.$)$

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