vtsnowedin wrote: All I am saying is that our rate of growth is declining so is no longer exponential
OK, the rate of growth is declining. Why not just stop there?
The time to double the population at 1% is a mere 70 years, that's just one lifetime. It surprises me that even here where we've been talking about compounding for coming on 2 decades the ramifications are still not clear. It is the
nature of the system that makes it act exponentially at whatever rate not the rate itself.
My point is there is no arbitrary cutoff that makes proportional growth or decline no longer proportional. Whatever the rate is
at any particular time, it's always acting on the whole. The whole is growing
today at about 1% rate, that means next year there will be 101% as many people, and whatever the rate at that time, it will act on the new total. That's what makes it exponential, not the rate, not some unspecified big-sounding number, not the hockey stick, but the compounding.
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself.
https://en.wikipedia.org/wiki/Exponential_growthIn mathematics, a quantity that grows exponentially is one that grows at a rate proportional to its size. This does not mean merely that for any exponentially growing quantity, the larger the quantity gets, the faster it grows. It implies that the relationship between the size of the dependent variable and its rate of growth is governed by a strict law, of the simplest kind: direct proportion.
...The phrase exponential growth is often used in nontechnical contexts to mean merely surprisingly fast growth. In a strictly mathematical sense, though, exponential growth has a precise meaning which does not necessarily mean that growth will happen quickly. In fact, a population can grow exponentially but at a very slow absolute rate (as when money in a bank account earns a very low interest rate, for instance),
https://academickids.com/encyclopedia/i ... ial_growthIn a linear function, the rate of change is constant. In an exponential function the rate of change is proportional
https://www.austincc.edu/agladish/Preca ... rowth.htmlBut importantly, as lucky said, exponentials also work in the negative.
The implication is since any population change
rate other than zero is exponential, as soon as the rate consistently falls below zero, decline will be exponential as well. Although as I mentioned earlier, birth rate must halve or death rate double before that can happen. (17.5 & 7.5 per thousand respectively I think it was)
Unless our chart turns into a logistics curve bumping against carrying capacity like most other living things seem to do. Personally I think that ship has sailed because we've been so good at exploiting nature. So exponential decay, likely far below our original carrying capacity it is.
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The legitimate object of government, is to do for a community of people, whatever they need to have done, but can not do, at all, or can not, so well do, for themselves -- in their separate, and individual capacities.
-- Abraham Lincoln, Fragment on Government (July 1, 1854)