Let's break down the given question step-by-step to find the correct answer.
### Step 1: Understanding the Table
The table provides data about the population of two countries, China and India, in two different years, 2010 and 2050. The key details from the table are:
- China:
- Population in 2010: 1,338,000,000
- Estimated population in 2050: 1,437,000,000
- India:
- Population in 2010: 1,189,000,000
- Estimated population in 2050: 1,748,000,000
### Step 2: Analyzing the Data
The data shows the estimated population figures for 2010 and the predicted figures for 2050. This suggests a comparison over time to understand future population trends.
### Step 3: Matching the Purpose
Given the options:
1. to predict the future populations of China and India
2. to present the populations of China and India when they were established
3. to compare a country with a large population to a country with a small one
4. to show how the population of two countries changed from long ago to today
### Step 4: Evaluating Each Option
- First Option: "to predict the future populations of China and India" — This aligns well with the data provided. The years 2010 and 2050 suggest that the table aims to show the future trends.
- Second Option: "to present the populations of China and India when they were established" — The year 2010 is recent, not aligned with when the countries were established, so this does not fit.
- Third Option: "to compare a country with a large population to a country with a small one" — Both China and India have very large populations, so this does not fit.
- Fourth Option: "to show how the population of two countries changed from long ago to today" — The table only shows a change from 2010 to 2050, not a long historical comparison, so this is not accurate.
### Final Decision
The most appropriate purpose of the table is:
To predict the future populations of China and India
This option concisely captures the essence of what the table is intended to do by providing a comparison of current and future population estimates for the two countries.
