A meteorologist measures the atmospheric pressure at altitude .

(a) Plot the points and use the regression capabilities of the graphing utility to find a linear model for the revised data points.

Construct a table with and values to calculate values.

Graph:

Plot the ponts .

Using regression capabilities graph thepoints.

Observe the graph:

The linear model equation is .

The linear Regression is in the form of ln P = ah + b

where P is the Pressure and h is the altitude.

To calculate the values of a and b

Therefore the linear regression is ln P = -0.1496h + 9.296

Graph

(b)

The linear model equation is .

Apply Exponent on both side

The exponential model equation is . \ \

(c)

Graph the Original Data and the Exponential Regression

(d)

Pressure

Apply derivative on each side with respect to .

\ \

If h = 5 then Rate of change of Pressure 

If height h = 5 km then Rate of change of Pressure is -771.40.

If h = 18 then Pressure 

If height h = 18 then Rate of change of Pressure is -110.39.

Therefore,

(a) Linear Regression is ln(P) = -0.1496h + 9.296

(b) Exponential Regression is 

(d) Rate of change of Pressure is -771.40 if h = 5 km.

Rate of change of Pressure is -110.39 if h = 18.