Your swimming pool containing 60000 gal of water has been contaminated by 6 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200 gal/min. Assume that the dye is uniformly distributed throughout the pool. (a) What is the intial value problem for the filtering process? Let q(t) be the amount of dye in the pool at any time t. What is the initial amount of dye in the pool? NOTE: Ențer the exact answer. Use q as g(t). dą grams dt min q(0) = grams (b) Solve for q(t) from part (a) q(t) = grams ||

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