$\"\"$

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 points $\"\"$ .

Using regression capabilities graph the points.

$\"\"$

Observe the graph:

The linear model equation is $\"\"$ .

$\"\"$

(b)

The linear model equation is $\"\"$ .

Exponentiate each side.

$\"\"$

The exponential model equation is $\"\"$ .

$\"\"$

(c) Graph the function: $\"\"$ .

Plot the points $\"\"$ .

Graph:

$\"\"$

(d)

Pressure $\"\"$

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

When $\"\"$ .

$\"\"$

$\"\"$ .

When height $\"\"$ then rate of change of Pressure is $\"\"$ .

When $\"\"$ .

$\"\"$

$\"\"$ .

When height $\"\"$ then rate of change of Pressure is $\"\"$ .

$\"\"$

(a) Graph:

$\"\"$

The linear model equation is $\"\"$ .

(b) The exponential equation is $\"\"$ .

(c) Graph:

$\"\"$ .

(d)

When height $\"\"$ then rate of change of Pressure is $\"\"$ .