Modeling processes with saturation Abbreviations:
DE Differential Equation
ODE Ordinary Differential Equation IC Initial Condition(s)
IVP Initial Value Problem

A tank with five-gallon capacity is filled at a constant rate of fifteen gallon per minute and

drained at the same rate.
The inflow has salt concentration of twenty grams of salt per gallon.
Once the incoming salt brine is in the tank, the instant mixing assumption is imposed. Initially, there is only pure water in the tank. But as the time passes, the amount of salt in

the tanks changes (we will express this amount in grams).
Set up and solve the ODE IVP in order to answer the questions:
(a) How much salt will we have in the tank after 3 minutes? [A]
(b) In the long run, how much salt do we expect the tank to contain? [B]
(c) How soon will the amount of salt in the tank reach half of its asymptotic value? [C]

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