[thaumasiotes]

> I don't think China wants back to exponential growth ever.

Any policy defined in terms of "X children per couple" or "X children per woman" is, by definition, exponential growth.

When X is 3, it's very rapid exponential growth.

[hackingthenews]

You are correct of course.

The 3 children per woman limit is still the smallest number that accommodates for the 2.1 average required for replacement level. To achieve equilibrium and avoid rapid growth the limit must be set to 3 and then hope that the average will be drawn down enough by the women who can't/won't have children for various reasons.

Not advocating for this policy, and I am not considering how well it works in practice and the morality. This is just a reductionist model.

[yakubin]

When X is 2, then 2 people replace 2 in theory, so there is no growth. In practice, some of those children will die early, so 2 is actually a minor reduction, not growth, forget about exponential.

[thaumasiotes]

When X is 2, you have one of the most important functions in the family of functions that display exponential growth. It is the one in which the exponent is 0.

> not growth, forget about exponential.

This is really weird phrasing, since you're on much stronger ground saying "not growth" [arguable] than you are "not exponential" [flat wrong]. I just pointed out that defining results in terms of "X children per woman" will always necessarily produce an exponential curve. That's the definition of an exponential curve. If you want to distinguish between "growth" and "decay", you can say so, but you're still stuck with labeling them "exponential growth" and "exponential decay".

[yakubin]

> When X is 2, you have one of the most important functions in the family of functions that display exponential growth. It is the one in which the exponent is 0.

This is technically correct, but also purely academic. If I called the function f(X) = 5 in an analysis exam "exponential", then I would be laughed out of this exam, and for a good reason.

> This is really weird phrasing, since you're on much stronger ground saying "not growth" [arguable] than you are "not exponential" [flat wrong].

"not A" implies "not (A and B)". That's all I meant.

[thaumasiotes]

> If I called the function f(X) = 5 in an analysis exam "exponential", then I would be laughed out of this exam

That's not true at all; you'd have to look at the context. If you called it an exponential function as part of a discussion of exponential functions, you'd raise no eyebrows.

Even if you were doing it in a weird way, it's unlikely you'd get laughed out of the room; math exams are not known for penalizing you for being correct.

[alva]

X = 1 is not exponential growth

[anoncake]

Sure it is: x = 1^t

[thaumasiotes]

Yes, it is. Since the population is shrinking over time, it is more often called "exponential decay", but mathematically there's no difference. It just means the value of the exponent is negative.

[beowulfey]

Some people pick the strangest hills to die on.

Per this argument, I would think that an exponential function is different to something experiencing exponential growth. One of them is a definition, the other is a description. They aren’t really interchangeable when it comes to communicating a point.