View source for Proof of slow linear growth instead of exponential in case of no children for people over 60 years old

'''Proof:'''<br/>
Let's denote y -- total population,  m -- young population under 60 years,  k1 is reproduction rate,  k2 is transition rate into group "over 60 years old".<br/>
y' = m<br/>
m' = k1 *m - k2 *m = 0 when k1=k2 (two children per family)<br/>
m' = 0 => m = const => '''y (total population) growth is linear'''<br/>

'''Another proof:'''<br/>
If population under 60 years old is constant and equals N, then number of people transitioned into "over 60 years old" group cannot exceed N for any consequent 60 years. That's because if we suppose contrary then when the youngest of them was born, the population of people under 60 would have exceeded N.<br/> Consequently, growth is linear and it's limited by N/60 * t.

Overall, the key is allowing to bear children only for constant number of people any time.<br/>
Linear population growth is stable: number of new people (who haven't their 2 children) is constant => growth remains to be linear.<br/>

'''Yet another proof:''' <br/>
UN [https://ourworldindata.org/future-population-growth#:~:text=The%20United%20Nations%20projects%20that,at%2010.4%20billion%20in%202100. states] that Earth population would stabilize near 10 billion people.<br/>
Every 60 years, about 10 billion people would be born, and about 10 billion people would die.

Let's consider what happens if humans become immortal.<br/>
Again, every 60 years, about 10 billion people would be born, however about 10 billion people would not die. (people after 60 years aren't allowed to bear children).<br/>
In 30 years, Earth population would be 20 billion people, in 90 years it would be 30 billion. It's '''slow linear growth instead of exponential''' one.<br/>
The result, of course, is valid not only at 10 billion primary population of the Earth, but also at any other value.<br/>
It will be necessary to increase the yield in 4/3 times in the first 30 years, in the next 30 years - in 5/4, then in 6/5, 7/6 and so on.

'''Note.'''<br/>
Of course, if we change the restriction "people after 60 years aren't allowed to bear children" <br/>
to restriction "anyone can have no more than 2 children per whole life", population growth can only become even more slow and remain linear.