The table below shows the saturated thickness (water level) in five-year intervals.
Water Levels in the Ogallala Aquifer
\begin{tabular}{|c|c|}
\hline Year & Saturated Thickness \\
\hline 1975 & $32.77 m(107.5 t )$ \\
\hline 1980 & $28.11 m(95.5 t )$ \\
\hline 1985 & $25.68 m(84.25 t )$ \\
\hline 1990 & $22.48 m(73.75 t )$ \\
\hline 1995 & $19.43 m(63.75 t )$ \\
\hline 2000 & $16.84 m(55.25 t )$ \\
\hline 2005 & $14.15 m(47.75 t )$ \\
\hline 2010 & $12.27 m(40.25 t )$ \\
\hline
\end{tabular}
If water continues to be used at the current rate, what will the saturated thickness be in 2020?
Answer (2)
Calculate the differences in saturated thickness between consecutive 5-year intervals.
Determine the average rate of change in saturated thickness per 5-year interval: approximately -2.93 m per 5 years.
Extrapolate the saturated thickness to 2015: 12.27 + ( − 2.93 ) = 9.34 m.
Extrapolate the saturated thickness to 2020: 9.34 + ( − 2.93 ) = 6.41 m. The saturated thickness in 2020 will be approximately 6.41 m.
Explanation
Analyzing the Data First, let's analyze the given data. We have the saturated thickness of water in the Ogallala Aquifer at 5-year intervals from 1975 to 2010. Our goal is to predict the saturated thickness in 2020, assuming the current rate of water usage continues. To do this, we'll look at the differences in saturated thickness between consecutive 5-year intervals to see if there's a trend.
Calculating Differences Now, let's calculate the differences in saturated thickness between consecutive 5-year intervals:
1980 - 1975: 28.11 − 32.77 = − 4.66 m 1985 - 1980: 25.68 − 28.11 = − 2.43 m 1990 - 1985: 22.48 − 25.68 = − 3.20 m 1995 - 1990: 19.43 − 22.48 = − 3.05 m 2000 - 1995: 16.84 − 19.43 = − 2.59 m 2005 - 2000: 14.15 − 16.84 = − 2.69 m 2010 - 2005: 12.27 − 14.15 = − 1.88 m
Calculating Average Rate of Change The differences are not exactly constant, but they are relatively close. To get a general idea of the rate of change, we can calculate the average rate of change:
Average rate of change = 7 ( − 4.66 ) + ( − 2.43 ) + ( − 3.20 ) + ( − 3.05 ) + ( − 2.59 ) + ( − 2.69 ) + ( − 1.88 ) = 7 − 20.5 ≈ − 2.93 m per 5 years.
Estimating Saturated Thickness in 2015 and 2020 Now, we can use this average rate of change to estimate the saturated thickness in 2015 and 2020.
Saturated thickness in 2015 = Saturated thickness in 2010 + Average rate of change Saturated thickness in 2015 = 12.27 + ( − 2.93 ) = 9.34 m
Saturated thickness in 2020 = Saturated thickness in 2015 + Average rate of change Saturated thickness in 2020 = 9.34 + ( − 2.93 ) = 6.41 m
Final Answer Therefore, if water continues to be used at the current rate, the saturated thickness in 2020 will be approximately 6.41 meters.
Examples
Understanding how water levels change over time helps us manage this precious resource better. For example, if we know the water level in a well is decreasing by about 3 meters every 5 years, we can predict when the well might run dry if we keep using water at the same rate. This helps us plan for water conservation and find new water sources to ensure we have enough water for the future. This is crucial for agriculture, drinking water, and maintaining healthy ecosystems.
If the current water usage continues, the predicted saturated thickness of the Ogallala Aquifer in 2020 will be approximately 6.41 meters. This was calculated by finding the average rate of change in thickness over previous years. Using this rate, we extrapolated values for 2015 and then for 2020.
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