What is the primary energy source for sprouting plants?

To what extent are young plants powered by the potential energy stored in the seeds and when does solar energy take over? Are there other energy sources involved?

I was observing sprouts in a germinator [is this a word?], pushing up the lid after being left alone over three-four days. As this is a considerable amount of work (for such young plants) I wondered how long the plant can access the original energy stored in the bean/seed and how it compares to the amount of energy it can get. As you can see in the picture, the sprouts have only access to water and some sunlight.

I suspect the potential energy it draws somehow decreases monotonically (perhaps linearly, quadratically, exponentially?) over time, while the solar energy pics up.

Is this mental model correct?
I'd appreciate an answer that a non-expert can understand.

I think these were radish sprouts, but my question is more general.

This depends largely on the plant, some seed stores can last a very long time, but a few general trends can be discussed.

sprouting plants run off stored carbohydrates in the seed, they are using respiration, photosynthesis begins as soon as they are able and they will switch over to it as quickly as possible it is however gradual as the plant never stops using respiration it just starts using photosynthetically produced sugars instead of stored ones. The stored energy will run out so the faster a plant can stop relying on it the better, so even a small production is helpful, you yest it is a gradual process, even if it is a fast gradual process ins some plants.

Your first question has an easy answer.

Q: "when does solar energy take over?"
A: as soon as a green part of the plant receives sunlight. Chlorophyll is the main light-harvesting pigment, and responsible for the green color of the plant.