- Define population growth as \(\text{Growth} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration})\).
- Calculate the growth for 2011 and 2012, which are both \(\text{Growth} = 1\).
- Test each of the four given 2013 scenarios against the target growth value of 1.
- Identify the correct option as \(\boxed{3 \text{ deaths, } 6 \text{ births, } 5 \text{ immigration, } 7 \text{ emigration}}\).
Explanation
- Analyzing the Data and Defining Growth
We are tasked with determining which set of population factors for 2013 results in the same net population growth as observed in 2011 and 2012. The net population growth is defined by the formula:
\[ \text{Growth} = (\text{Births} + \text{Immigration}) - (\text{Deaths} + \text{Emigration}) \]
We are provided with the data for 2011 and 2012 and four potential scenarios for 2013. We first need to calculate the growth for 2011 and 2012 to establish the target value.
- Calculating Growth for 2011 and 2012
For 2011, the data is: Deaths = 2, Births = 5, Immigration = 6, Emigration = 8.
Using the growth formula:
\[ \text{Growth}_{2011} = (5 + 6) - (2 + 8) = 11 - 10 = 1 \]
For 2012, the data is: Deaths = 1, Births = 4, Immigration = 1, Emigration = 3.
Using the growth formula:
\[ \text{Growth}_{2012} = (4 + 1) - (1 + 3) = 5 - 4 = 1 \]
Since both years resulted in a population growth of 1, our target growth for 2013 is 1.
- Evaluating 2013 Options
We now evaluate each of the four provided options for 2013 to see which one yields a growth of 1.
- 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 Option 2 results in a population growth of 1.
- Conclusion
The population growth in 2011 and 2012 was 1. By evaluating the provided options for 2013, we find that the combination of 3 deaths, 6 births, 5 immigration, and 7 emigration leads to the same growth. Thus, the correct option is the second one: 3 deaths, 6 births, 5 immigration, 7 emigration. Therefore, the result is \(\boxed{3 \text{ deaths, } 6 \text{ births, } 5 \text{ immigration, } 7 \text{ emigration}}\).
Examples
This math concept can be applied to wildlife conservation and resource management, where biologists track population changes to understand how different factors like migration, birth rates, and death rates contribute to overall trends. By calculating the net growth, they can model future scenarios and make informed decisions on how to stabilize or support vulnerable populations. This ensures that conservation efforts are data-driven and effective.