Problem 5. During droughts, water for irrigation is pumped fromthe ground. When ground water is pumped excessively, the watertable lowers. In California, lowering water tables have been linkedto reduced water quality and sinkholes. A particular well inCalifornia’s Inland Empire has been monitored over many years. In1994, the water level was 250 feet below the land surface. In 2000,the water level was 261 feet below the surface. In 2006, the waterlevel was 268 feet below the surface. In 2009, the water level was271 feet below the surface. In 2012, it was 274 feet below thesurface. And in 2015, it was 276 feet below the surface. (a) Find acubic (degree 3) polynomial model for this data on water level.First, define what x and y mean here, and write the data points youuse. Then, find a cubic which is a best fit for this data, in theleast squares sense. (b) Use your model to predict the water levelof the well, in feet below the surface, in 2020. You may assumethat the trends of 1994 to 2015 continue to 2020.
