Winter_Light

 For once, we are escaping a Winter wallop lightly:

                                                                                 

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Hydro-Quebec is currently stopped from charging more that 3% more for a given year,

no matter how bad inflation might get. But for someone with a fixed income, there are still

challenges. It is the same with rent; every year the baseline is the current rent which is then

inflated). Chatted with Copilot about getting clear on the math in all this. Below:

The situation is, and I am using 100$ to illustrate, that I am getting an increase of 3% every year, including year 1. So year to year, what costs me 100$ in year 1 is now costing me more. And there is an increase of 3% on that amount...

Perfect — thanks for clarifying. You’re saying the increase applies starting in year 1 itself, so the $100 is not a fixed baseline, but already subject to the 3% growth each year. Let’s lay this out carefully.

                                                                                     

✅ So the difference is subtle:

If you treat year 1 as $100 flat, the total was $309.09.

If you treat year 1 as already increased by 3%, the total is $318.36.

Would you like me to also show you a side-by-side table for 10 years so you can see how quickly the compounding adds up?

Yes...

Great — let’s build that 10‑year side‑by‑side table so you can see the compounding clearly when the 3% increase applies starting in year 1.

                                                                                              

✅ Key takeaway:

Each year’s bill grows by 3% on the previous year.

After 10 years, the annual bill is $134.39.

The total across 10 years is about $1,181.70.

Would you like me to also plot this as a graph (year vs. cost) so you can visually see the curve of compounding growth?

Here’s the visual you asked for: the line chart shows how your utility bill grows over 10 years with a 3% annual increase starting in year 1.

                                                                                      

                                                                            

🔎 What the chart shows

Year 1: $103 (already includes the 3% increase)

Year 5: $115.93

Year 10: $134.39

The curve rises smoothly because each year’s bill compounds on the previous year. It’s not a straight line — it’s exponential growth.

💵 Total over 10 years

Adding all yearly costs together gives about $1,181.70 spent in total. That’s nearly 18% more than if the bill had stayed flat at $100 per year.

📌 Key takeaway

This chart makes clear how even a modest 3% annual increase steadily compounds into a significant difference over time. By year 10, your bill is more than 34% higher than the original baseline.

Could you define this curve as a pure exponential, so I can see it in online... 

Yes — the curve you’re describing is pure exponential growth. Let’s define it cleanly so you can plug it into any online graphing tool (like Desmos, GeoGebra, or WolframAlpha).

                                                                               

...

Asked Copilot to give me a version of the graph on base-e. Below:

                                                                                    

                                                                                             

They appear identical; are they?

Excellent observation — yes, they appear identical, and here’s why:

                                                                                                  

✅ Bottom line: They are mathematically identical at integer years, but the base‑𝑒

 form is more flexible because it extends naturally to fractional years and calculus 

operations.