The tank has 100 gal of water and 50 oz of salt. Water having the salt concentration of 1/4 (1+\cos t) oz/gal flows into tank at the rate of 2 gal / min, and mixture in tank flows out at the rate of 1 gal / min.
i) Determine amount of salt in tank at any time.
ii) Long-time behavior of solution is the oscillation about the certain constant level. Determine level? Find amplitude of oscillation?