A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows into the tank at the rate of 5 gallons per minute, and the well stirred mixture flows out of the tank at the rate of 5 gallons per minute. Find the amount of salt in the tank after 8 minutes.

The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

, where .

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is:

answer: the answer is simply nothing.

step-by-step explanation: because there is no ending to this question

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