Arguing about how to express that is sort of pointless.
It is in fact a logistic sigmoid function. It is amazing, in that it is not what you'd expect : clearly the vast majority of species have the ability to correctly estimate the carrying capacity of a habitat and only overshoot by a little bit.
So the Malthusian argument is incorrect, probably, if humans are like other animals (and since population growth curves in many localities do indeed look like S-curves I would say that this ought to be the default claim). Human population size will by itself stop just shy of the carrying capacity of the planet. Which is exactly what you'd want to happen.
In all likelihood, this will happen without active measures from governments (which won't work anyway due to the global nature of the required policies), with or without popularizing contraceptives, with or without female labor participation, ... (not saying those aren't desirable, just that they aren't necessary)
The alternative requires an assumption that humans are hugely different from the species that we evolved from, and since this certainly isn't true in the biological sense, why would our population growth be so very different ? Humans are not the first large animal to "conquer the planet", and reach population numbers in the billions, with some fish well on the way to trillions even today, and we aren't the biggest species in terms of total biomass by a very long way (amongst non-plants that honour likely goes to ants, but even pathetic species of bacteria dwarf their numbers). Will we be the last one ? Perhaps, but it seems unlikely.
https://en.wikipedia.org/wiki/Logistic_function#In_ecology:_...
It's very likely that humans exhibit the same behavior, but on a micro-scale, this isn't very comforting. If a politician says "Well, the earth will be fine, but 10% of you are gonna die and another 30% won't be able to have children that survive to adulthood", there would be rioting on the streets ... which has a non-negligible chance of bringing about those numbers.
Nature will be just fine, but remember that the mechanisms by which nature self-adapts are the four horsemen of the apocalypse: pestilence, war, famine, and death.
> The alternative requires an assumption that humans are hugely different from the species that we evolved from
Well we are, for proof look at the fact that we're even discussing it here when all the other species never did. Look, that all sounds very peachy if it weren't for the fact that our species alone has grown the brains and the self-justifications for consciously attempting to continously outwit "nature" (and be able to replicate way beyond what our ancestral habitats could carry) at every turn with agriculture and all the sciences =) granted, there's no point in or way of "going back" for all manner of reasons, but we needn't lose sight of certain basic facts here..
https://ourworldindata.org/world-population-growth/
Growth is clearly exponential. Your theories don't fit the data.
Can you explain what I'm missing ?
Look at the linear function. It experiences "decrease in the rate of growth" along the line.
If the exponent is not constant, we do not have "exponential growth" anymore — by definition.
A growth curve that is, in fact, logistic, would look like that.
It's been continuously declining for half a century after peaking, the assumption that it's suddenly reached a bottom at the most recent measurement and returned to an exponential steady state is unwarranted.
In this case G is the difference between the birth rate and the death rate for time period t. As long as a G is positive, you get exponential growth. Every time. This is how compound interest works. The fact that your balance next year is based on your starting balance + the balance multiplied by a positive growth rate ALWAYS leads to exponential growth in the balance.
Here's a video that explains it. https://www.youtube.com/watch?v=NB4KVSjgi24
OK then. Let the birth rate be 1 person per second and death rate 0 (nobody dies). Do you get exponential growth? No. This is still linear growth.
Your another mistake is that ax^b is exponential growth, and ax^c is also exponential growth (if b and c are constants), but these are different processes. If you get a single process with changing exponent, this is no longer exponential growth, it can be arbitrarily defined.
One person per second is linear.
.00001 person per year * current population is exponential, assuming only that the (fractional) person is added to the population factor so that the base is bigger next year.
If you don't understand that, you shouldn't be commenting on growth rates.
If you assume the growth rate is exponential, then you will see that the first year, the growth rate is 100%, the second year the growth rate is 50%, the third year the growth rate is 33% and so on. At any point, you can fit an exponential to the graph tangential to the current point. It won't fit much, but you can still do it.
A decreasing exponential may be exponential, but it also very well may not be. But we'll need to look a few years into the future to be sure. That said, expert opinion seems to be that growth rate is at this point linear (or iow an exponential that decreases each year so as to appear linear) [0]
[0]: https://ourworldindata.org/wp-content/uploads/2013/05/update...
No, a "decreasing exponential" is not exponential. It might return to an exponential after the decreasing period, but during the period of decline, the growth is not exponential.
Look at [0]. 2016 had a higher population than 2015, yet the growth was smaller. Not just a smaller percentage, but actually smaller by about half a million people. If growth was exponential, then the higher population would have a larger increase, but it doesn't, and so the growth isn't exponential.
[0]: http://www.worldometers.info/world-population/world-populati...
You are describing the shift from a steep exponential growth curve to a lower exponential growth curve that I mentioned earlier.
If you get 10% compounded interest on your money it grows exponentially at 10%.
If you get 9% compounded interest it grows exponentially at 9%.
And if you _were_ getting 10% and the bank changes the rate to 9% your money is now growing exponentially at 9% interest, assuming only that the interest is reinvested.
Then going from $100 to $110 that would be 10%.
Going from $110 to $120 would be ~9%.
Going from $120 to $130 would be ~8%.
In any year you could conclude my savings grow exponentially. 10%! 9%! whoohoo! But if you look over a longer time frame, it clearly isn't.
And as nevdka mentioned, the population growth is less than linear. If my bank gave me $10 of interest last year and $9 this year, and $8 the next, there is definitely no exponential growth.