People who say that we cannot continue to grow our economy point out that N is constant and once you reach a point where At = 1, Yt will not be able to increase. However, this argument fails, because it does not take into consideration Tt. Why does this matter? Lets look at a couple of examples.
Two thousand years ago it would have been impossible to build a tractor to increase the agricultural output of your land. Even if you had the same amount of iron, copper and other natural resources, you still could not make those resources as productive as a tractor. Even if we held the amount of natural resources constant, transforming them into a tractor would make them significantly more productive and more valuable. Essentially, we have held N and At constant and increased Tt, which has increased Yt.
What about other resources, such as oil. We are currently using oil and turning it into other things, like CO2 through the use of internal combustion engines, which may be causing N to actually decrease over time. However, over time Tt has increased as well. We can now go farther and do more with a gallon of oil than we could have before. Lets say that we have used about half of the oil that is in the Earth. does this mean that we can only do half as much? Of course not. If over this time we doubled the efficiency of our oil use, we have essentially not changed the productive capacity of our resources. Essentially, we have slightly decreased N, but Yt was able to increase, due to Tt increasing as well.
The model presented here is quite basic. If fails to take into consideration that each of the variables may be dependent on each other as well. For example, it is quite possible that by using the resources we are causing Tt to increase at a faster rate than it would have otherwise. If this is the case, the use of resources helps us to develop new ways of conserving the resource as well. The only question to our ability to continue to grow our economy forever would be: can Tt continue to increase? At this point, I only see evidence that Tt is actually increasing faster now than it has in the past, and I don't see any reason why it cannot continue to increase for any significant amount of time.