Time lapse involves shooting frames at a speed much slower than the standard (let say 16 frames per second), perhaps as slow as one per day or much faster perhaps one per second. Then playing the frames at a normal rate of 16 per second or somewhat slower.
There are 326 calories in 1 piece (1/10 of 1-layer, 8 or 9 dia) of Carrot Cake with Icing. Calorie breakdown: 45% fat, 51% carbs, 4% protein.
But generally, I would say, for a standard 9 cake, divided in 6, one of those slices will be about 500-600 vcals, but keep in mind, it is  considered a better for you cake, just don;'t eat too much!! Probably that little slice alone had roughly 150 calories in it, but enjoy it your birthday only comes once a year. I wouldn't really worry about the caloric intake in the cake...worry about the fat that you are consuming. There are lots of food out there that are low in calorie, but high in fat.