$\"\"$

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(a)

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Graph the model: $\"\"$ .

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The result shows an error message.

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Because the function $\"\"$ is undefined at $\"\"$ .

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The domain of the logarithm function contains only positive real numbers.

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Therefore, the $\"\"$ is undefined at $\"\"$ .

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(b)

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Find the line equation using excel sheet method.

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Graph :

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Plot the points and draw a regression equation.

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$\"\"$

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Observe the graph:

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The equation model is $\"\"$ .

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(c)

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Graph:

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Plot the points and graph the equation.

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$\"\"$

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(d)

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Estimate the altitude when $\"\"$ .

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The equation for altitude is $\"\"$ .

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Substitute $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , the altitude is $\"\"$ kilometers.

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(e)

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Estimate the pressure when $\"\"$ .

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The equation model for pressure is $\"\"$ .

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Substitute $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply exponential on each side.

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$\"\"$

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$\"\"$ .

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When $\"\"$ the pressure is $\"\"$ atmospheres.

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(f)

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The rate of change of pressure is $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .