Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). Suppose: • The vat c

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Consider A Large Vat Containing Sugar Water That Is To Be Made Into Soft Drinks See Figure Below Suppose The Vat C 1 (290.53 KiB) Viewed 40 times

Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). Suppose: • The vat contains 200 gallons of liquid, which never changes. • Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe B into the vat at the rate of 15 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 45 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: ds 405 S dt OM 40 (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) 1800 Ke 40 o (C) Suppose that there are 38 tablespoons of sugar in the vat at t = 0. How many tablespoons will be present 3 minutes later? 864.17 x tablespoons INI