Based on this data, predict what will happen to the water in the Ogallala aquifer over the next decade.
| Year | Saturated Thickness (feet) |
|------|----------------------------|
| 1975 | 107.5 |
| 1980 | 95.5 |
| 1985 | 84.25 |
| 1990 | 73.75 |
| 1995 | 63.75 |
| 2000 | 55.25 |
| 2005 | 47.75 |
| 2010 | 40.25 |
A. The water will continue to increase.
B. The water will continue to decrease.
C. The water will remain the same.
D. The water will be completely depleted.
Answer (1)
Calculate the differences in saturated thickness between consecutive years.
Determine the average rate of change of the saturated thickness.
Use linear regression to project the saturated thickness in 2020.
Based on the projected thickness, conclude that the water will continue to decrease. T h e w a t er w i ll co n t in u e t o d ecre a se .
Explanation
Understanding the Problem We are given data showing the saturated thickness of the Ogallala aquifer (in feet) for various years from 1975 to 2010. Our goal is to predict what will happen to the water in the aquifer over the next decade (2010-2020).
Calculating Thickness Differences First, let's calculate the difference in saturated thickness between consecutive years to see how the water level is changing.
Determining the Rate of Change The differences in saturated thickness between consecutive years are:
1975-1980: 107.5 − 95.5 = − 12 feet 1980-1985: 95.5 − 84.25 = − 11.25 feet 1985-1990: 84.25 − 73.75 = − 10.5 feet 1990-1995: 73.75 − 63.75 = − 10 feet 1995-2000: 63.75 − 55.25 = − 8.5 feet 2000-2005: 55.25 − 47.75 = − 7.5 feet 2005-2010: 47.75 − 40.25 = − 7.5 feet
Calculating the Average Rate of Change The differences are not constant, but they show a decreasing trend in the rate of decline. To get an estimate, we can calculate the average rate of change over the given period. The average rate of change is approximately -9.61 feet per 5 years (or -1.92 feet per year).
Projecting the Saturated Thickness in 2020 Now, let's project the saturated thickness in 2020 using a linear regression model. Using the data, we find the linear equation that best fits the data is:
y = − 1.9202380952380176 x + 3897.0744047617477
Where x is the year and y is the saturated thickness. Plugging in 2020 for x , we get:
y = − 1.9202380952380176 ∗ 2020 + 3897.0744047617477 = 18.193452380952294
Predicting the Future Based on this projection, the saturated thickness in 2020 is estimated to be approximately 18.19 feet. Since the saturated thickness is still positive, the water will continue to decrease, but it will not be completely depleted in the next decade.
Final Answer Therefore, based on the data, the water in the Ogallala aquifer will continue to decrease over the next decade.
Examples
Understanding the rate at which a natural resource like the Ogallala aquifer is depleting helps in making informed decisions about water conservation and management. For example, farmers can use this information to optimize irrigation techniques, and policymakers can implement regulations to control water usage. By analyzing historical data and predicting future trends, communities can develop sustainable practices to ensure the long-term availability of this vital resource. This type of analysis is also crucial for planning infrastructure projects and managing water resources in other regions facing similar challenges.
