To determine which scenario maintains the same population change in 2013 as in 2012, we need to first calculate the population change for the years 2011 and 2012, and then identify which option achieves the same population change in 2013.
### Step-by-Step Solution:
1. Calculate Population Change for 2011:
- Deaths in 2011: 2
- Births in 2011: 5
- Immigration in 2011: 6
- Emigration in 2011: 8
- Population change formula: \( \text{(Births + Immigration) - (Deaths + Emigration)} \)
- Population change for 2011: \( (5 + 6) - (2 + 8) = 11 - 10 = 1 \)
2. Calculate Population Change for 2012:
- Deaths in 2012: 1
- Births in 2012: 4
- Immigration in 2012: 1
- Emigration in 2012: 3
- Population change formula: \( \text{(Births + Immigration) - (Deaths + Emigration)} \)
- Population change for 2012: \( (4 + 1) - (1 + 3) = 5 - 4 = 1 \)
3. Desired Population Change for 2013:
- We want to maintain the same population change in 2013 as in 2012: \( \text{Population Change = 1} \)
4. Evaluate Each Option for 2013:
- Option 1:
- Deaths: 4
- Births: 7
- Immigration: 2
- Emigration: 6
- Population change: \( (7 + 2) - (4 + 6) = 9 - 10 = -1 \)
- Option 2:
- Deaths: 3
- Births: 6
- Immigration: 5
- Emigration: 7
- Population change: \( (6 + 5) - (3 + 7) = 11 - 10 = 1 \)
- This matches the desired population change of 1.
- Option 3:
- Deaths: 5
- Births: 2
- Immigration: 8
- Emigration: 3
- Population change: \( (2 + 8) - (5 + 3) = 10 - 8 = 2 \)
- Option 4:
- Deaths: 1
- Births: 5
- Immigration: 3
- Emigration: 7
- Population change: \( (5 + 3) - (1 + 7) = 8 - 8 = 0 \)
Among these options, only Option 2 maintains the same population change of 1 as in 2012.
### Conclusion:
To maintain the population growth of cheetahs in 2013 the same as the previous years, the population change needs to be the same as it was in 2012. Based on the provided options, the correct answer is Option 2: 3 deaths, 6 births, 5 immigration, 7 emigration.
