Scoping Cat Litter: Linear or Exponential?

If you have co-inhabited with a cat you are likely to be familiar with the joys of scoping cat litter. I have shared my house with cats for the greater part of my life and I’m well used to being on cat litter duty. When we transitioned from a single cat to four, the requirements of the job seemed to increase exponentially. This feeling was only reinforced with the latest to additions which bring the grand total to a whopping six cats to two humans. The cat to human ratio has seen a great shift, from an original 1:2 ratio in favor of humans, to the current 6:2 ratio giving the cats a clear victory over the humans. All cats use the litter boxes (note the plural) in a fairly equal amount with minor fluctuations in frequency and quantity, therefore it is possible to talk about the average use of any cat as “c” where c = 1 solids and 3 liquids uses per day.
This is clearly a simple linear function, where the number of “c” (cats) will determine the number of “items” (“I”) to be scooped out daily.
Formula: I= (1+3)c with an I intercept of 0 (no cats, no items to be scooped).
When I think about this problem logically I know the above equation to be sound and what is more, true. But I must admit, it feels like the number of items I must scooped daily increases exponentially. I scoop the litter boxes when I get up before getting in the shower. The cats are very grateful and happy to have clean boxes, so they immediately use them again. Second round of scooping has to take place right after breakfast. By the time I get back home, is time for the third pass over them. And somehow between then and bedtime the items in those magic boxes multiply themselves in such fashion that a fourth and final scooping has to take place before going to bed. This is one example of how easily we can be fooled by our perception of a quantity even when we know its true magnitude.