4. A tank initially contains 400 gal of fresh water. At timet = 0, a brine solution with a concentration of 4 lb of salt per gallon enters the tank at a rate of 2.5 gal/min and the well- stirred mixture flows out at a rate of 4 gal/min. (a) How long does it take to empty the tank? (b) Set up the initial value problem whose solution, x(t), represents the amount of salt in the tank, and indicate the time interval on which this IVP is valid. (c) How much salt is present when the tank contains 100 gal of brine?
4. A tank initially contains 400 gal of fresh water. At timet = 0, a brine solution with a concentration of 4 lb of salt per gallon enters the tank at a rate of 2.5 gal/min and the well- stirred mixture flows out at a rate of 4 gal/min. (a) How long does it take to empty the tank? (b) Set up the initial value problem whose solution, x(t), represents the amount of salt in the tank, and indicate the time interval on which this IVP is valid. (c) How much salt is present when the tank contains 100 gal of brine?
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Transcribed Image Text:4. A tank initially contains 400 gal of fresh water. At time t = 0, a brine solution with a
concentration of 4 lb of salt per gallon enters the tank at a rate of 2.5 gal/min and the well-
stirred mixture flows out at a rate of 4 gal/min.
(a) How long does it take to empty the tank?
(b) Set up the initial value problem whose solution, x(t), represents the amount of
salt in the tank, and indicate the time interval on which this IVP is valid.
(c) How much salt is present when the tank contains 100 gal of brine?
(d) What is the maximum amount of salt present in the tank during the time
interval? When is this maximum achieved?
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