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 yeras, the average family has 4 children, and the average couple begins having children at age 20 and ends at 30.
I guess this is assuming that no one moves in or out, since the problem says nothing about it. Can someone please tell me how to figure this out?
It is not possible to solve without a lot of assumptions
1) when is the average child born to the the couple (age, not range of 20 to 30), and what is the deviation of that, and the deviation of the birth of the other kids. A distribution over 10 generations of ten years makes a big difference.
Do the offspring reproduce? The problem does not state.
What is the moving in/moving out.
What is the deviation on the life expenctancy? Ie, how many die before entering reproductive years?
What is the deviation on the gender birth rate...ie, the folks who cant find a mate? Do they get to reproduce?
this type of problem is explored extensivly in texts on Population genetics.
To calculate the population of an area after a given period of time, we need to make some assumptions and simplifications as you mentioned. Let's make a few assumptions to solve this problem:
1. We assume that the couples will stay in the area for 200 years without anyone moving in or out.
2. We assume that all couples will have their first child at age 20 and have a total of 4 children by the time they turn 30.
3. We assume that the children will not reproduce.
4. We assume that there is an equal number of males and females in each couple.
Given these assumptions, let's calculate the population after 200 years step by step:
1. We start with 20 individuals (10 couples) moving into the area.
2. Each couple will have 4 children, so after the first generation, the total population will be 20 (initial couples) + 10 (couples' children) = 30.
3. As we assume the children won't reproduce, the population remains at 30 in the subsequent generations.
4. Since the average life expectancy is 60 years, and each couple moves in at age 20, we can assume that after 40 years (60 - 20), the initial couples will pass away. However, their children will remain.
5. After 80 years (40 years for the first generation and 40 years for the second generation), the children will also pass away, but their grandchildren will remain.
6. This process continues, and after 200 years, only the original couples' great-great-grandchildren will still be alive.
To calculate the population after 200 years, we calculate the number of generations that have passed. Since each generation is 40 years (20 years for parents and 20 years for their children), we divide 200 by 40, which gives us 5 generations.
Population after 200 years = Initial population + (Number of children per couple * Number of couples * Number of generations)
Population after 200 years = 30 + (4 * 10 * 5) = 30 + 200 = 230
Therefore, after 200 years, the population in the area, based on these assumptions, would be 230 individuals.