Your goal is to build a simple spreadsheet model to estimate

$C{O}_2$ emissions $($tons$)$ in a given year from the North

Carolina's light duty vehicle sector. Light duty vehicles include

passenger cars and light trucks. Please apply the techniques for

mastering complexity that were described in Module $1.$ Once

developed, you will use your model to estimate current and future

emissions under different scenarios. For the problem above,

develop a tree diagram following the format in the assigned reading

presented in class. $($An example for a different problem is shown on the $......,$

a$.$ Post an image$/$screenshot of your tree diagram.

b$.$ Enter the parameter that sits at the top of your tree diagram.

c$.$ Enter each of the "leaves" under the goals. $($If you have multiple levels, only enter the first set. For

the unrelated sample diagram, this would mean entering "width," "height," and "thickness."$)$

d$.$ Make a baseline numerical estimate for each term in the tree diagram $($all leaves$),$ and annotate with a

justification for this value. The justification can include a literature reference or a description of a

bottom$-$up calculation. These values should be thoughtful and plausible, but you will not be

evaluated on accuracy. The baseline year is $2024.$ Post an image$/$screenshot of the tree diagram,

now populated with numbers and references.

e$.$ Enter your estimate for the total $C{O}_2$ emissions in $2024$ from the NC light duty vehicle fleet in

terms of tons$/$year$.$

f$.$ Implement your model in an organized and well labeled Excel spreadsheet and develop it in a way

that allows you to easily change key parameters. The top of your Excel spreadsheet should have a

block of parameters and assumptions for your model that is well$-$labeled $($e$.$g$.,$ lbs $C\frac{O_2}{g}$allon, mean

mpg for vehicles, etc.$)$ You need to turn in your spreadsheet, and we will check its functionality.

g$.$ Based off your model, estimate the amount of total $C{O}_2$ emissions $($tons$)$ in a given year from the

entire US light duty vehicle sector using an invariant and proportional reasoning.

h$.$ Define your invariant used for part g$.$

i$.$ Can you use an invariant to extend this model beyond the US$?$ Why or why not?

j$.$ In June $2024,$ as part of the U$.$S$.$ Department of Transportation, the National Highway Traffic

Safety Administration issued new vehicle fuel economy standards. These standards, which apply to

both passenger cars and light$-$duty trucks, will bring the light$-$duty vehicle fuel economy up to $50\mathrm{.}4$

miles per gallon for the $2031$ model year fleet. Assume that this policy is achieved and the average

fuel economy of all $2031$ model year cars and light$-$duty trucks sold is $50\mathrm{.}4$ miles per gallon. Also

assume that this fuel economy target is based on dynamometer testing in a laboratory environment

and the real on$-$road fuel economy will likely be $80\%$ of this target. Use your model to estimate total

$C{O}_2$ emissions from light duty vehicles in $2050$ for North Carolina, when we can assume that most

of the vehicles on the road will have been purchased post$-2031.$ What was the percentage increase

$($use positive value$)$ or decrease $($negative value$)$ of total emissions in $2050$ relative to your $2024?$

$($Hints: Did the total number of vehicles on the road change from $2024$ to $2050?$ Why? Do people

drive less or more in $2050$ compared to $2024?$ Why?$)$

k$.$ List the parameters that changed in your model for part $($j$)$

What is one example of structural uncertainty in your model?

m$.$ Parametric uncertainty?

I$\text{'}$d really love help figuring out how to get this set up in excell. The tree diagram the questions mentioned at the top. is just side ways version of the one shown.

Here is a picture of the kind of tree diamgram he wants