What will my population be in 1,000 years?

[annab]

If I have a starting population of 200 people with an average life expectancy of 35 and a yearly growth rate of .10, what will my population be in 1,000 years?

 

[Joppy]

If I have a starting population of 200 people with an average life expectancy of 35 and a yearly growth rate of .10, what will my population be in 1,000 years?

Welcome to MHB!

Have you made any progress on the exercise? Anything in particular that you are struggling with?

 

[S.G. Janssens]

with an average life expectancy of 35

Could it be that the answer depends on how the survival time is assumed to be distributed?

 

[annab]

Joppy

I haven’t made any progress on this problem, I don’t know where to start.

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Krylov

I don’t understand, can you explain the possible distributions to me and show me how to do it?

 

[I like Serena]

Joppy

I haven’t made any progress on this problem, I don’t know where to start.

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Krylov

I don’t understand, can you explain the possible distributions to me and show me how to do it?

Hi annab! Welcome to MHB!

So we start with 200 people.
What will happen in the first year if no one dies?
That is, how many people will be born?
And how many people might we expect to die in the first year?

 

[tkhunny]

Average Lifetime of 35 years:
1) 1/2 die immediately and 1/2 die in 70 years.
2) Everyone lives exactly 35 years.
3) Deaths occur uniformly between 25 and 45 -- ~20 per year.
4) Infinitely many other possibilities.

We are told the ORIGINAL population has an average lifetime of 35 years. We are not told ANYTHING about those joining the group. If joining the group is defined as a birth process, it is very unlikely to support the assumption that new entrants have the same life expectancy as the original population.

More information or let's state the assumptions!

 

[I like Serena]

Average Lifetime of 35 years:
1) 1/2 die immediately and 1/2 die in 70 years.
2) Everyone lives exactly 35 years.
3) Deaths occur uniformly between 25 and 45 -- ~20 per year.
4) Infinitely many other possibilities.

We are told the ORIGINAL population has an average lifetime of 35 years. We are not told ANYTHING about those joining the group. If joining the group is defined as a birth process, it is very unlikely to support the assumption that new entrants have the same life expectancy as the original population.

More information or let's state the assumptions!

My interpretation: it just means that on average 1 person in 35 dies every year.
I believe the actual age distribution is not really relevant. And without information saying otherwise we should assume that the death rate is constant.

 

[tkhunny]

My interpretation: it just means that on average 1 person in 35 dies every year.
I believe the actual age distribution is not really relevant. And without information saying otherwise we should assume that the death rate is constant.

No objection. As long as we know its an ASSUMPTION. There is NOTHING in the problem statement that demands that it be so. We should also be careful not to conflate mortality rates with future life expectation. Since we are given expected future lifetime, we may have jumped a bridge inadvertently.