How the power law model has evolved

Hey everyone, just wanted to share some analysis I did on how the famous power law model has shifted over the years. I can't post images here, so you'll need to click the links if you're interested. Maybe a mod can help out since this is legit info and not spam. So, the power law comes from the idea that when you plot the USD/BTC ratio (aka price) on a log-log graph, it kinda looks linear overall, like this: https://i.ibb.co/674TFLzJ/Screenshot-From-2026-01-25-18-40-29.png The red line is just a linear fit done with the least squares method to all the data. As of January 25, 2026, this fit is represented by: https://i.ibb.co/Pz3tKmwD/image.png In simple terms, it says that the price of 1 Bitcoin in USD equals the number of days since January 3, 2009, raised to the power of 5.7, multiplied by 0.0000000000000000291. This is pretty cool because it gives us a basic equation that the USD/BTC ratio fluctuates around. You might wanna consider extending this into the future: https://i.ibb.co/PJs470b/image.png But here's what I'm really curious about: how reliable is this extrapolation? Before jumping to say it's impossible, please take a minute to read on. Now, let's analyze this a bit. Imagine someone in 2016 used this model to predict future prices. How accurate would they have been? The chart below shows the model's extrapolation based on data before January 2016, compared to what really went down after that: https://i.ibb.co/GQy60VfC/image.png You can do this for different time frames too.