Reading the Wikipedia article on hyperbolic discounting it seems like there is some evidence for a quasi-hyperbolic discounting. Looking at the formula, the interpretation is exponential discounting for all future times considered but with a special treatment of the present.

How to explain this? It is not unlikely that the brain uses one system for thinking about now and another about the future. Considering the usual workings of evolution, the latter is most likely a much later feature than the former. Considering this, one could perhaps even argue that it would be surprising if there wasn't any differences between the systems.

There seems to be some literature referenced at the wiki article. I suggest looking into it if you are interested. I sadly don't have the time right now.