Suppose a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t = 0, we begin dumping 2 gallons per minute of salt solution containing 0.25 pounds of salt per gallon into the tank. Also at time t = 0, we begin removing 1 gallon per minute of salt water from the tank. As usual, suppose the water in the tank is well mixed so that the salt concentration at any given time is constant throughout the tank. i) Set up an initial value problem for the amount of slat in the tank. ii) What is your model equation when V0 = 0? Comment on the validity of the model in this situation. What will be the amount of salt in the tank at time t for this situation?

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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.