Math puzzle: Filling a bath tub with increasingly smaller containers

We are trying to fill a bath tub! How long does it take if we make our containers smaller and smaller following a certain pattern? Finding an upper and lower bound means finding a range of possible answer: we can know that it will take more than a certain amount of pours and less than a certain amount of pours, which will at least give us an idea. Who can come up with the most precise range? Grappling this problem will introduce you to ideas within Calculus. The situation is super counter intuitive. Good luck!