Carrots are a storage crop, and prefer a cool, dark, and moist place. They will get soft if they start to loose moisture; store either in a covered container in the fridge with a wet cloth, or even in a container of moist clean sand in a pantry space. Depending on your storage method, they can last anywhere from a couple weeks to a couple months. The more mature the carrots are, the longer they will last also.
We have a few different ways we like to prepare carrots at Wellspring!
The New Whole Foods Encyclopedia by Rebecca Wood
Asparagus to Zucchini by Fairshare Coalition
Produce: A fruit and vegetable lover's guide by Bruce Beck
The Art of Fermentation by Sandor Elix Katz
Our own experience!