When you think of it, you quickly realize that exposure gets longer very fast.
The best way I have to put it is using the cream cheese example. If you have a tablespoon of cheese and you spread it on a cracker, you get a lot of cheese on it. But if you take the same tablespoon of cheese and you spread it on toast, you have a lot less because you have a greater surface to cover. It's the same thing with light. If you expose a 1 cm square of film, you have a lot of light hitting it. but if you expose a 2cm square, you have 4 times less... and so on. 3cm drops to 9 times less... exposure decreases according to surface and is exponential.