A large vat contains 100 liters of pure water. Salt and water are then added to the tank: salt at a rate of 8 ounces per minute, and water at a rate of 5 liters per minute. Simultaneously, the saltwater solution is drained from the bottom of the vat at a rate of 5 liters per minute. Assume the saltwater is kept thoroughly mixed. a. Write an initial-value problem that gives the amount of salt in the vat after t minutes. (hint: your answer should be separable so that you can solve in part (b)) b. Solve the initial-value problem you gave in part (a).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.