Expert: Paul Klarreich - 1/29/2007

Question
Hi! I need help solving a problem actually for my chemistry class, although that problem isn't about chemistry. I don't know exactly what math it is, but hopefully you can help me! Here's the problem:

If 10 human couples move into a new unpopulated area, how many people will live in the area after 200 years? The couples are 20 years old when they move. The people's life expectancy is 60 years, the average family has 4 children, and the average couple begins having children at age 20 and ens at 30.

Answer
Questioner:  Stephanie
 
Question:  
Hi! I need help solving a problem actually for my chemistry class, although that problem isn't about chemistry. I don't know exactly what math it is, but hopefully you can help me! Here's the problem:

If 10 human couples move into a new unpopulated area, how many people will live in the area after 200 years? The couples are 20 years old when they move. The people's life expectancy is 60 years, the average family has 4 children, and the average couple begins having children at age 20 and ends at 30.
................................
Hi, Stephanie,

There are a lot of complications here, but I am going to adopt the usual practice of scientific math -- OVERSIMPLIFY LIKE HELL. (excuse me, I mean LIKE HECK)

So if a couple produces four children at an average age of 25, they are producing two new couples each generation, which is 25 years.  (We will worry about deaths later.

So in the year 200, we will have had 8 generations, and in each, the number of new couples produced is twice the previous one.  That means that the 8th generation produced 2^8 times the original 10, or 2560 couples.

We had new generations produced in Years:

1: 0 to 10
2: 25 to 35
3: 50 to 60, etc.
...
6: 125 to 135
7: 150 to 160
8: 175 to 180.

Now, since the life expectancy is 60 years, year 200 will see only those born in the last two generations:

8: 2560 couples, ready to start reproducing, but not doing it yet.
7: 1280 couples.

So the answer to that is 2560 + 1280 = 3840 couples.

As I said, this oversimplifies like....