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.

Question

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.

Are you assuming that no one moves away and no one moves in?

If so -- then the population doubles every 25 years.

Thanks!! i guess it's assuming no one moves away and no one moves in, because that's all it said in the problem. but how did you figure out that it doubles every 25 years??

and so is the answer 5120 people??

Answer 1

To figure out the population growth in this scenario, we can use the information provided.

First, let's calculate the number of children each couple has during their childbearing years. Since the average family has 4 children, and childbearing starts at age 20 and ends at 30, there are 10 years for childbearing. Hence, each couple will have 4 children within those 10 years.

Since there are 10 couples, there will be a total of 10 * 4 = 40 children born.

Now, let's consider the population growth over time. The initial population is 20 (the 10 couples) * 2 (assuming each couple consists of one male and one female) = 40 individuals.

According to the assumption given, the population doubles every 25 years. So after 25 years, the population will be 40 * 2 = 80 individuals.

After another 25 years (50 years total), the population will double again to 80 * 2 = 160 individuals.

This doubling process continues every 25 years. After 75 years, the population will be 320 individuals, after 100 years it will be 640 individuals, and so on.

Now, the last doubling occurs after 175 years (seven cycles of 25 years). At this point, the population will be 320 * 2 = 640 individuals.

Finally, after 200 years, there will be another doubling, resulting in 640 * 2 = 1280 individuals.

So, based on the given assumptions, after 200 years, there will be a total of 1280 individuals living in the area.

Therefore, the answer is not 5120 people, but rather 1280 people.