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To predict the population in 2025 based on the given data, we can use a linear regression model or observe the trend to estimate the value.

### Data Summary:
- 1990: 92
- 1995: 81
- 2000: 71
- 2005: 59
- 2010: 51

Let's calculate the equation of the line that best fits this data and use it to predict the population in 2025.

### Step-by-Step:
1. **Define the years relative to 1990 as `x` values:**
   - 1990: \(x = 0\)
   - 1995: \(x = 5\)
   - 2000: \(x = 10\)
   - 2005: \(x = 15\)
   - 2010: \(x = 20\)

2. **Define the corresponding population values `y`:**
   - 1990: \(y = 92\)
   - 1995: \(y = 81\)
   - 2000: \(y = 71\)
   - 2005: \(y = 59\)
   - 2010: \(y = 51\)

Now, we will use linear regression to find the best-fitting line for this data, then use the line's equation to predict the population in 2025 (which corresponds to \(x = 35\)).

I'll calculate this now.The predicted population in 2025 is approximately 18.8 (rounded to one decimal place).

This estimation is based on the observed linear trend of population decline over the years from 1990 to 2010.

Would you like more details on how this calculation was performed, or do you have any other questions?

Here are some related questions you might be interested in:
1. How would the prediction change if we used a different type of regression (e.g., exponential)?
2. What would be the population in any given year, such as 2030 or 2040?
3. Can we visualize the population trend using a graph?
4. How sensitive is this prediction to changes in the data?
5. What assumptions are we making by using a linear model?

**Tip:** For better predictions, consider using more data points or applying a model that reflects the nature of the data more closely, like exponential decay for declining populations.

Learn how to predict the population in the year 2025 based on past data using linear regression. This problem involves key mathematical concepts such as linear regression and trend analysis, suitable for students in Grades 9-12.

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