Estimate the number of people since ever?

This is definitely a top-down (as opposed to bottom-up) sizing.First, I'll assume homo sapiens.

There's a lot of ways to approach this, but I would personally segment it by world population over time. I know that population growth is exponential, and I roughly know the population in different periods - however I have to be careful to account for "existence" i.e. birth/generations.

A lifespan is around 70, but I'll round down to 50 (which averages out across all of time).

• I know there's about 7 billion people today.
• Going back 50 years (1960s) there were around 4 billion.
• 50 years again (1910s) that was around 2 billion
• Now I'll keep that # but double the count to 100 years (in 1800s, 2 billion people). I.e. population was around a billion, but lets count it twice to account for births.
• In 1700s, down to 1 billion (again, population of around 500 million?)
• And I'll keep this 500 million x 7 down to the 1st millenium (3.5 billion).
• Now, I'll drop it to mellenium, and keep 500 million down to when "civilization" emerged, around 4,000 BC. So, 500 million X 5 = 2.5 billion.
• Then, we're into an extremely long tail for hundreds of thousands of years but very low population, so I'll throw in another 500 million.

If I were to draw this on a chart, it'd be exponential, so I'd a least be comfortable with that.

I'll add 7+4+2+2+3.5+2.5+.5 = 31 Billion people.

However, I know that, for most of history, death rates were absolutely horrid and that something like 50% of all people died before the age of 7. So, I'll multiply 31 billion by 1.5 to get the answer: 46.5 billion people have existed in the world.

Am I close?

(editiert)