A Tank Is Filled with 200 Gallons of Brine in Which

question 154

Essay

A tank is filled with 200 gallons of brine in which is dissolved 5 pounds of salt. Brine containing 0.1 pound of salt per gallon enters the tank at a rate of 2 gallons per minute, and the well-stirred mixture is drawn from the talk at the same rate.(a) Find the amount of salt in the tank at time $t$ .(b) How much salt is present in the tank after 20 minutes?
(c) How much salt is present after a long time? What is the concentration then?

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Definitions:

Cognitive Restructuring

A psychotherapeutic process of learning to identify and dispute irrational or maladaptive thoughts known as cognitive distortions.

Systematic Desensitization

A therapeutic technique used to reduce phobia or anxiety through gradual exposure to the feared object or situation.

Enclosed Space

A physical area that is surrounded by boundaries which can be natural or man-made, limiting access and egress.

Psychotherapist

A professional who treats mental health issues by psychological rather than medical means, often through talking therapies.