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Question: your swimming pool containing 70000 gal of water has been...

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Your swimming pool containing 70,000 gal of water has been contaminated by 7 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 250 gal/min. Assume that the dye is uniformly distributed throughout the pool.

(a) What is the initial 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 the dye in the pool?

Enter the exact, fully simplified answer. Use q as q(t).

dq/dt = ____ g/min

q(0) = _____ grams

(b) Solve for q(t) from part (a).

Do not use thousands separator in the answer field.

q(t) = _____ grams

(d) Find the time T at which the concentration of the dye first reaches the value of 0.02 g/gal.

Round your answer to two decimal places.

T = _____ hours

(e) Find the flow rate r that is sufficient to achieve the concentration 0.02 g/gal within 4 h.

Round your answer to the nearest integer.

r = _____ gallons/minute

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