The populations and areas of four states are shown.
| | Population | Area ($km^2$) |
| :------ | :---------- | :------------ |
| State A | $1,055,173$ | 2,677 |
| State B | $1,333,089$ | 36,418 |
| State C | $3,596,677$ | 5,543 |
| State D | $6,745,408$ | 10,555 |
Which statement regarding these four states is true?
A. The state with the lowest population has the greatest population density.
B. The state with the second lowest population has the lowest population density.
C. The state with the lowest population has the lowest population density.
D. The state with the second greatest population has the lowest population density
Answer (1)
Calculate the population density for each state by dividing its population by its area.
Compare the calculated population densities to determine the lowest and highest densities.
Identify the state with the second-lowest population.
Verify that the state with the second-lowest population indeed has the lowest population density, confirming the correct statement: The state with the second lowest population has the lowest population density.
Explanation
Understanding the Problem We are given the populations and areas of four states and asked to determine which statement about their population densities is true. Population density is calculated by dividing the population of a state by its area.
Calculating Population Densities First, we calculate the population density of each state:
State A: Population Density = 2 , 677 1 , 055 , 173 ≈ 394.16 people per k m 2 State B: Population Density = 36 , 418 1 , 333 , 089 ≈ 36.61 people per k m 2 State C: Population Density = 5 , 543 3 , 596 , 677 ≈ 648.87 people per k m 2 State D: Population Density = 10 , 555 6 , 745 , 408 ≈ 639.07 people per k m 2
Analyzing the Statements Now, let's analyze the given statements:
The state with the lowest population has the greatest population density. State A has the lowest population (1,055,173). Its population density is approximately 394.16. State C has the greatest population density (648.87). So, this statement is false.
The state with the second lowest population has the lowest population density. State B has the second lowest population (1,333,089). Its population density is approximately 36.61, which is the lowest among the four states. So, this statement is true.
The state with the lowest population has the lowest population density. State A has the lowest population, but its population density (394.16) is not the lowest. So, this statement is false.
The state with the second greatest population has the lowest population density State C has the second greatest population, but its population density (648.87) is not the lowest. So, this statement is false.
Conclusion Therefore, the true statement is: The state with the second lowest population has the lowest population density.
Examples
Understanding population density is crucial in urban planning and resource management. For instance, knowing the population density of different regions helps in allocating resources like water, electricity, and transportation effectively. High population density areas may require more infrastructure and services compared to sparsely populated regions. This concept is also used in environmental studies to assess the impact of human populations on ecosystems.
