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 the population by the area.
State A: Density ≈ 394.16, State B: Density ≈ 36.61, State C: Density ≈ 648.87, State D: Density ≈ 639.07.
Compare the calculated densities to the given statements.
The state with the second lowest population (State B) has the lowest population density.
The final answer is: The state with the second lowest population has the lowest population density.
Explanation
Problem Analysis We are given the populations and areas of four states and asked to determine which statement about their population densities is true. To do this, we need to calculate the population density of each state and then compare them.
Calculating Population Densities The population density of a state is calculated by dividing its population by its area. So, we have:
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.
The state with the lowest population is State A (1,055,173). Its population density is 394.16, which is not the greatest.
The state with the second lowest population has the lowest population density.
The state with the second lowest population is State B (1,333,089). Its population density is 36.61, which is the lowest.
The state with the lowest population has the lowest population density.
The state with the lowest population is State A (1,055,173). Its population density is 394.16, which is not the lowest.
The state with the second greatest population has the lowest population density.
The state with the second greatest population is State C (3,596,677). Its population density is 648.87, which is not the lowest.
Conclusion Based on our calculations and analysis, the correct statement is:
The state with the second lowest population has the lowest population density.
Examples
Understanding population density is crucial in urban planning. For example, knowing the population density of different areas helps city planners allocate resources effectively, such as schools, hospitals, and transportation. A higher population density might require more schools and public transportation options in that area. This concept is also used in environmental studies to assess the impact of human populations on ecosystems.
