- The net population growth is calculated as: \(\text{Growth} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration})\).
- In both 2011 and 2012, the growth was \(1\).
- We test each given option for 2013 and find that only the option with 3 deaths, 6 births, 5 immigration, and 7 emigration results in a growth of \(1\).
- The correct choice is \(\boxed{3 \text{ deaths, } 6 \text{ births, } 5 \text{ immigration, } 7 \text{ emigration}}\).
Explanation
- Data Analysis and Growth Formula Verification
We analyze the population changes of a cheetah population over several years. The net population growth is determined by the balance between factors that increase the population (births and immigration) and factors that decrease the population (deaths and emigration). Specifically, the growth formula is given by:
\[\text{Growth} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration})\]
According to the provided data for 2011:
- Births = 5
- Immigration = 6
- Deaths = 2
- Emigration = 8
Calculating the growth for 2011: \((5 + 6) - (2 + 8) = 11 - 10 = 1\).
According to the provided data for 2012:
- Births = 4
- Immigration = 1
- Deaths = 1
- Emigration = 3
Calculating the growth for 2012: \((4 + 1) - (1 + 3) = 5 - 4 = 1\).
Since the growth for both years was 1, our goal is to find which option for 2013 results in a net growth of 1.
- Evaluating the 2013 Scenarios
We test each option to determine which one results in a net growth of 1 using the formula: \(\text{Growth} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration})\).
- Option 1: 4 deaths, 7 births, 2 immigration, 6 emigration.
\(\text{Growth} = (7 + 2) - (4 + 6) = 9 - 10 = -1\).
- Option 2: 3 deaths, 6 births, 5 immigration, 7 emigration.
\(\text{Growth} = (6 + 5) - (3 + 7) = 11 - 10 = 1\).
- Option 3: 5 deaths, 2 births, 8 immigration, 3 emigration.
\(\text{Growth} = (2 + 8) - (5 + 3) = 10 - 8 = 2\).
- Option 4: 1 deaths, 5 births, 3 immigration, 7 emigration.
\(\text{Growth} = (5 + 3) - (1 + 7) = 8 - 8 = 0\).
Comparing the results, only the second option yields the required net population growth of 1.
- Conclusion
Based on our evaluation, the only scenario that maintains the consistent population growth of 1 is the one with 3 deaths, 6 births, 5 immigrations, and 7 emigrations. Thus, the correct option is the second one: \(\boxed{3 \text{ deaths, } 6 \text{ births, } 5 \text{ immigration, } 7 \text{ emigration}}\).
Examples
This type of population analysis is essential for conservationists monitoring endangered species like cheetahs. By calculating net population growth, researchers can understand whether a population is stable, increasing, or declining due to environmental pressures or human impacts. If a population consistently grows by a specific number, authorities can use this data to predict future trends and determine if interventions like habitat protection or breeding programs are necessary to maintain the ecosystem's health.