To determine during which of the given 50-year intervals the world's population increased the most, we need to look at the population increases for each interval.
1. Interval 1950-2000:
- Population in 1950: 2.52 billion
- Population in 2000: 6.14 billion
- Increase: [tex]\( 6.14 - 2.52 = 3.62 \, \text{billion} \)[/tex]
2. Interval 1800-1850:
- Population in 1800: 1.00 billion
- Population in 1850: 1.26 billion
- Increase: [tex]\( 1.26 - 1.00 = 0.26 \, \text{billion} \)[/tex]
3. Interval 1850-1900:
- Population in 1850: 1.26 billion
- Population in 1900: 1.65 billion
- Increase: [tex]\( 1.65 - 1.26 = 0.39 \, \text{billion} \)[/tex]
4. Interval 1900-1950:
- Population in 1900: 1.65 billion
- Population in 1950: 2.52 billion
- Increase: [tex]\( 2.52 - 1.65 = 0.87 \, \text{billion} \)[/tex]
Now, we need to compare these increases:
- For the interval 1950-2000, the increase is 3.62 billion.
- For the interval 1800-1850, the increase is 0.26 billion.
- For the interval 1850-1900, the increase is 0.39 billion.
- For the interval 1900-1950, the increase is 0.87 billion.
By comparing these values, we can see that the greatest population increase occurred during the interval [tex]\(1950-2000\)[/tex] with an increase of 3.62 billion.
Therefore, the world's population increased the most in interval [tex]\( \boxed{1950-2000} \)[/tex].
