To determine the best approximate population density of a major U.S. city with a population of 8,550,405 people and a land area of 1,213.4 square kilometers, we need to follow these steps:
1. Calculate the Population Density:
Population density is determined by dividing the total population by the land area. Mathematically, it can be expressed as:
[tex]\[
\text{Population Density} = \frac{\text{Population}}{\text{Land Area}}
\][/tex]
Plugging in the values given:
[tex]\[
\text{Population Density} = \frac{8,550,405}{1,213.4}
\][/tex]
2. Evaluate the Population Density:
Performing the division:
[tex]\[
\text{Population Density} \approx 7046.65 \frac{\text{people}}{\text{km}^2}
\][/tex]
3. Compare with Given Options:
We will now compare our calculated density value (approximately 7046.65 people per square kilometer) with the provided options to find the closest match:
- Option 1: [tex]\(7047 \frac{\text{people}}{\text{km}^2}\)[/tex]
- Option 2: [tex]\(7124 \frac{\text{people}}{\text{km}^2}\)[/tex]
- Option 3: [tex]\(7167 \frac{\text{people}}{\text{km}^2}\)[/tex]
- Option 4: [tex]\(7500 \frac{\text{people}}{\text{km}^2}\)[/tex]
4. Determine the Closest Option:
Comparing all the options, the closest population density to our calculated value of approximately 7046.65 people per square kilometer is:
[tex]\[
7047 \frac{\text{people}}{\text{km}^2}
\][/tex]
Hence, the best approximate population density of the city is:
[tex]\[
7047 \frac{\text{people}}{\text{km}^2}
\][/tex]
