# Differential Equations and Rate of Change

A tank initially contains 100 gallons of a solution that holds 10 pounds of a chemical. A solution containing 1 pound of the chemical runs into the tank at a rate of 4 gallons per minute, and the well-mixed mixture runs out of the tank at a rate of 6 gallons per minute.

a. How much chemical is in the tank after 25 minutes?

b. How much chemical is in the tank after 50 minutes?

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A tank initially contains 100 gallons of a solution that holds 10 pounds of a chemical. A solution containing 1 pound of the chemical runs into the tank at a rate of 4 gallons per minute, and the well-mixed mixture runs out of the tank at a rate of 6 gallons per minute.

Let x(t) (pounds) be the chemical in the tank at time t (minutes).

And V(t) be the total volume of the solution in the tank.

First ...

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