When will the Amish population growth rate slow down?

[Agafin]

It has to at some point, right?  But looking at the data, their population growth rate doesn't appear to be slowing down so far, still hovering well above 3%, with a fertility rate above 7 children per woman. But how sustainable is this? There are 360 000 of them and at the current rate (doubling of their population in less than two decades), they will reach over 1 million people by 2050 and over 6 million by 2100. At that point, Midwestern and New England states like Ohio or Pennsylvania would be experiencing population booms the likes of which they haven't had in centuries. But this all seems impossible so when do you think their population growth will start declining? And what will be the cause?

Normally, decline in birth rates occur when countries get more developed and women get educated. But given that these people live in North America which has already undergone that transformation and yet they managed to resist it, can it still happen to them?