correction to my first post.

put everything into a spreadsheet so that when I found errors I could quickly recalculate.....

Draft:

See attached PDF

My calculus chops are not what they were, but it seems right. Note that these are annual revenue (trillion $/year) reported annually - so the simple sum is very close to the cumulative value - picture a bar graph compared to your fitted curve; the area of each bar is revenue per year times one year. That is probably close enough if you need to do it on the fly, and intuitive to an audience.

Yes, like this below. polynomial curve fit approximated by series of bars.

Corrected the x-axis label from 2-32, should have been 0-30, from 2020-2030.

Here is the graph of cumulative net revenue over 30 years.

Looks like an "S" curve, and based on the shape of the annual amount.

You should not have to do that step - the series of bars approximating the polynomial you estimated from a series of numbers. Those bars are (if you space by one year) a way of estimating the numbers you started with. You can just use the En-ROADS output directly - as an approximation, it is not as good as your fitted polynomial integration, but good enough.

Note that the underlying model uses numerical approximations for every integration or accumulation in the system. We use an eighth-year time step, but otherwise, adding the output is the same way we would calculate in the software if we had a cumulative net revenue graph

Yes, and the source of the data was EN-ROADS by downloading the data from the graph to my spreadsheet and then doing all the calculations and graphing in the spreadsheet.

Yes, some of my calculations and graph are repetitive steps.

Thanks for confirming that I'm on the right track with these calculations.

Next steps are to share this with others in Zoom meetings.

And this has lead me to think of other ideas to engage with local elected officials.

thanks Charles.

Take Care

## Richard Turnock