You need more sample points, larger multipliers, or prior expectation of seeing an exponential curve to see that as exponential growth.
What? The former is exponential and the latter is linear. They are the definition of different.
The 30th number in the first series is 536870912.
The 30th number in the second series is 59.
You can't say just from 4 data points. Real data is noisy. Imagine each number is ±1.
I agree that it's worthwhile intuition in many cases, but really not here and even people equipt with both the data and the mathematical expertise to use it there have also made many bad calls on this.