Exercises 3.2fndx(t). We can determine the concentration oF salt in the frst tank by dividingx(t)bytheits volume, i.e.,x(t)/60 kg/gal. Note that the volume oF brine in this tank remains constantbecause the ﬂow rate in is the same as the ﬂow rate out. Thenoutput rate1= (3 gal/min)·±x(t)60kg/gal²=x(t)20kg/min.Since the incoming liquid is pure water, we conclude thatinput rate1=0.ThereFore,x(t) satisfes the initial value problemdxdt= input rate1−output rate1=−x20,x(0) =x0.This equation is linear and separable. Solving and using the initial condition to evaluate thearbitrary constant, we fndx(t)=x0e−t/20.Now, lety(t) denote the mass oF salt in the second tank at time
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.