Your report should show enough detail that a reader could reproduce similar results with their own data. For items in which the prompt calls for an explanation and$/$or comparison, your response should include full sentences. However, an extensive narrative is not required.

Any responsive tables and plots should be incorporated into your report document. Your report should be submitted as a single PDF document. Do not include the text from this prompt in your report.

Each individual will$-$receive their own data.

Items for Report

Use the given data to estimate the rate of change of atmospheric pressure with respect to altitude at different heights over the range covered by the data. Include a table in your response.

Construct a function that models the given pressure$-$altitude data. Create a plot that includes both $($a$)$ the model function $($i$.$e$.,$ a curve representing the graph$)$ and $($b$)$ the data $($appearing as 'dots' on the plot$).$ Explain briefly how you chose your model function, including the values of any parameters.

Use your model function $($from Part $2)$ to compute a formula for the rate of change of atmospheric pressure with respect to altitude.

Together on the same plot, show the rate of change of atmospheric pressure with respect to altitude $($i$)$ as estimated directly from the data $($i$.$e$.,$ result of Part $1$ as 'dots'$),$ and $($ii$)$ also as calculated from with the model function $($i$.$e$.,$ the result of Part $3$ as curve$).$

Compare the rate of change you estimated directly from the data $($Part $4.$i$)$ with the rate of change you computed from the model function $($Part $4.$ii$).$ Use this comparison to assess your model function. Briefly state your observations and any conclusions.

$50\mathrm{.}6740\mathrm{.}2$

$101\mathrm{.}8729\mathrm{.}2$

$148\mathrm{.}4712\mathrm{.}8$

$198\mathrm{.}4689\mathrm{.}5$

$299\mathrm{.}9666\mathrm{.}9$

$398\mathrm{.}4659\mathrm{.}4$

$498\mathrm{.}8647\mathrm{.}6$

$997\mathrm{.}8530\mathrm{.}6$

$1501\mathrm{.}0431\mathrm{.}7$

$1991\mathrm{.}7361\mathrm{.}5$

$2491\mathrm{.}4295\mathrm{.}6$

$2991\mathrm{.}4251\mathrm{.}5$

$3505\mathrm{.}4206\mathrm{.}8$

$3996\mathrm{.}9172\mathrm{.}5$

$4999\mathrm{.}4121\mathrm{.}0$

$5992\mathrm{.}583\mathrm{.}0$

$7005\mathrm{.}258\mathrm{.}2$

$7994\mathrm{.}739\mathrm{.}4$

$9009\mathrm{.}827\mathrm{.}4$

$9998\mathrm{.}818\mathrm{.}5$

Altitude $($meters$)$ Pressure $($torr$)$