Learning curves can be fitted well with standard psychometric curves, like the Weibull function.
I decided to also post an answer here myself, as I've been working on the data after the answers came in. I accepted Bryan's answer as they rightfully suggested that these data should not be fitted with a simple exponential, but with a ...
You could use something like Desmos to rapidly try out different functions and see how well they fit the different datasets you have.
The site allows you to vary different function parameters using sliders and see how the shape changes in response.
For example, here's a plot using Demos that reproduces the shape of the curve used to fit the data in Fig 1 ...
Is your objective to model:
the decline in incremental daily learning over time, or
the total cumulative learning,
My feeling is that this problem is better modelled by thinking of the problem as modelling the decline in incremental daily learning over time.
There are two reasons for my assertion:
The decline in daily learning accords more with reality, ...
Sigmoids are more general and probably better for modeling learning than a simple exponential. Your exponential fits decently, but it probably doesn't describe the actual underlying process very well.
Importantly, learning is often not fastest at the start, there is often some level of "aha!" moment later on. Sigmoids can capture this.
There are a ...