If humans were biologically immortal, but had an average lifespan of 100 years, what would the distribution of ages be?

Let's say that humans were biologically immortal. Once they reach adulthood, they effectively stop aging. Due to disease though, the average lifespan is 100 years. (In practice, your access to healthcare would have a huge effect on your lifespan, but we'll ignore that for the purpose of this question, since it would make it much more difficult to answer.) For ease of answering this question, we'll say that distribution of lifespans is exactly an exponential distribution with mean 100 years.

Additionally, humans have hit the carrying capacity of the Earth, and so only reproduce to replace those who died. In particular, we'll assume that some sort of steady-state has been reached.

My question is, given these constraints, what would be the distribution of ages be? Basically what I'm looking for is an equation or graph that tells you how many people are at a given age.

Note that I'm talking about the current age, not the lifespan.

posted almost 6 years ago

PyRulez‭

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