To predict the future thickness of the water level in the Ogallala Aquifer, we can use linear regression based on the given data points. Here is a detailed step-by-step solution:
1. Collect the data points:
```
Year: 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010
Thickness: 107.5, 95.5, 84.25, 73.75, 63.75, 55.25, 47.75, 40.25
```
2. Fit a linear regression model:
We need to find a linear relationship between the year and the saturated thickness. The linear model can be represented as:
```
Thickness = slope Year + intercept
```
3. Determine the slope and intercept:
Using the least squares method (which minimizes the sum of the squares of the residuals), we find:
```
slope ≈ -1.9202381
intercept ≈ 3897.0744
```
4. Predict the thickness for the year 2020:
Plug the year 2020 into the linear equation:
```
Thickness_2020 = slope 2020 + intercept
Thickness_2020 ≈ -1.9202381 2020 + 3897.0744
Thickness_2020 ≈ 18.193452380951385
```
Therefore, the saturated thickness in the year 2020 is approximately 18.19 feet.
5. Predict the thickness for the year 2030:
Similarly, plug the year 2030 into the linear equation:
```
Thickness_2030 = slope 2030 + intercept
Thickness_2030 ≈ -1.9202381 * 2030 + 3897.0744
Thickness_2030 ≈ -1.0089285714288962
```
Therefore, the saturated thickness in the year 2030 is approximately -1.01 feet. This negative value indicates that the aquifer would be virtually depleted by 2030 if the trend continues.
Conclusion:
Based on the data and the linear regression model, the water level in the Ogallala aquifer is predicted to decrease significantly over the next decade, reaching approximately 18.19 feet by 2020. By 2030, the aquifer might be almost entirely depleted, indicating a severe reduction in water availability. Thus, the initial statement that the water will continue to increase is incorrect; in reality, it will continue to decrease.
