Your swimming pool containing 70000 gal of water has been contaminated by 10 kg

Question

Your swimming pool containing 70000 gal of water has been contaminated by 10 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 water to the pool at a flow rate of 250 gal/min. Write down the initial value problem for the filtering process, where q(t) is the amount of dye in the pool at any time t (in minutes). [Give exact coefficients (in form of fraction if needed).] Solve this initial value problem. Find to 2 decimal places the time T at which the concentration of dye first reaches the value c0 = 0.017 g/gal.

Explanation / Answer

k = -1 / 280

b) q(t) = 10 e^(-t / 280)

d) 1785.60

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