To analyze the data provided about the saturated thickness of the Ogallala aquifer and make predictions about its future, we can follow these steps:
1. List the given data:
- Years: 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010
- Saturated Thickness (feet): 107.5, 95.5, 84.25, 73.75, 63.75, 55.25, 47.75, 40.25
2. Calculate the rate of decrease in saturated thickness over each 5-year period:
- From 1975 to 1980: [tex]\(107.5 - 95.5 = 12\)[/tex] feet
- From 1980 to 1985: [tex]\(95.5 - 84.25 = 11.25\)[/tex] feet
- From 1985 to 1990: [tex]\(84.25 - 73.75 = 10.5\)[/tex] feet
- From 1990 to 1995: [tex]\(73.75 - 63.75 = 10\)[/tex] feet
- From 1995 to 2000: [tex]\(63.75 - 55.25 = 8.5\)[/tex] feet
- From 2000 to 2005: [tex]\(55.25 - 47.75 = 7.5\)[/tex] feet
- From 2005 to 2010: [tex]\(47.75 - 40.25 = 7.5\)[/tex] feet
3. Calculate the average rate of decrease per 5 years:
[tex]\[
\text{Average rate of decrease per 5 years} = \frac{12 + 11.25 + 10.5 + 10 + 8.5 + 7.5 + 7.5}{7} \approx 9.607
\][/tex]
4. Predict the decrease over the next decade (10 years):
[tex]\[
\text{Predicted decrease over 10 years} = 9.607 \times 2 \approx 19.214
\][/tex]
5. Predict the thickness of the aquifer in 2020 and 2030:
- Thickness in 2010: 40.25 feet
- Thickness in 2020: [tex]\(40.25 - \left(\frac{19.214}{2}\right) \approx 40.25 - 9.607 = 30.643\)[/tex] feet
- Thickness in 2030: [tex]\(40.25 - 19.214 = 21.036\)[/tex] feet
6. Determine the state of the aquifer:
- Since the predicted thickness in 2030 is 21.036 feet, which is greater than zero, the water will continue to exist but will decrease further.
Based on these calculations, the prediction for the Ogallala aquifer over the next decade is that the water will continue to decrease. Hence, the correct option is:
- The water will continue to decrease.
