Answer :
To determine the most likely population of City 3 according to the rank-size rule, follow these steps:
1. Understand the Rank-Size Rule: This rule suggests that the population of a city is inversely proportional to its rank in the population hierarchy. In simpler terms, if you list the cities in order of population size, each city's population should ideally be proportional to the inverse of its rank.
2. Given Populations:
- City 1: 1.2 million
- City 2: 900,000
- City 4: 100,900
- City 5: 440,000
3. Estimation Method:
- To estimate City 3's population, we can look at the populations of the nearby ranks:
- City 2 (Rank 2) has 900,000 people.
- City 4 (Rank 4) has 100,900 people.
- City 5 (Rank 5) has 440,000 people.
4. Calculate the Estimated Population for City 3:
- We take an average value for City 3's population based on the populations of the nearest known cities, specifically between the higher-ranked City 2 and the lower-ranked City 5.
To do this, we average the populations of City 2 and City 5:
[tex]\[ \text{Estimated Population of City 3} = \frac{\text{Population of City 2} + \text{Population of City 5}}{2} \][/tex]
[tex]\[ \text{Estimated Population of City 3} = \frac{900,000 + 440,000}{2} = 670,000 \][/tex]
Hence, the most likely population of City 3 according to the rank-size rule is 670,000. Thus, the correct answer is:
c. 600,000
1. Understand the Rank-Size Rule: This rule suggests that the population of a city is inversely proportional to its rank in the population hierarchy. In simpler terms, if you list the cities in order of population size, each city's population should ideally be proportional to the inverse of its rank.
2. Given Populations:
- City 1: 1.2 million
- City 2: 900,000
- City 4: 100,900
- City 5: 440,000
3. Estimation Method:
- To estimate City 3's population, we can look at the populations of the nearby ranks:
- City 2 (Rank 2) has 900,000 people.
- City 4 (Rank 4) has 100,900 people.
- City 5 (Rank 5) has 440,000 people.
4. Calculate the Estimated Population for City 3:
- We take an average value for City 3's population based on the populations of the nearest known cities, specifically between the higher-ranked City 2 and the lower-ranked City 5.
To do this, we average the populations of City 2 and City 5:
[tex]\[ \text{Estimated Population of City 3} = \frac{\text{Population of City 2} + \text{Population of City 5}}{2} \][/tex]
[tex]\[ \text{Estimated Population of City 3} = \frac{900,000 + 440,000}{2} = 670,000 \][/tex]
Hence, the most likely population of City 3 according to the rank-size rule is 670,000. Thus, the correct answer is:
c. 600,000
