(1 point) A pond contains 2300 L of pure water and an uknown amount of an undesirable chemical. Water contaninig 0.06 kg of this chemical per liter flows into the pond at a rate of 3 L/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Let Q(t) be the amount of chemical (in kg) in the pond at time t hours. (a) Write a differential equation for the amount of chemical in the pond? at any time time (enter Q for Q(t): dQ/dt = (b) How much chemical will be in the pond after a long time? Q_inf = (kg) (c) Does the limiting value in part (b) depend on the amount that was present initially? no
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Since the water entering the pond contains 0.06 kg of the chemical per liter and flows at a rate of 3 L/h, the rate of the chemical entering the pond is: 0.06 kg/L * 3 L/h = 0.18 kg/h Now, we need to find the rate at which the chemical is leaving the pond. Since Show more…
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Section 1.1 Direction Fields: Problem 12 (1 point) A pond contains 1000 L of pure water and an uknown amount of an undesirable chemical. Water contaninig 0.06 kg of this chemical per liter flows into the pond at a rate of 5 L/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Let Q(t) be the amount of chemical (in kg) in the pond at time t hours. (a) Write a differential equation for the amount of chemical in the pond? at any time time (enter Q for Q(t): dQ/dt = (b) How much chemical will be in the pond after a long time? Q_inf = (kg) (c) Does the limiting value in part (b) depend on the amount that was present initially? no
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The pond initially contains 4,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.04 grams of this chemical per gallon flows into the pond at a rate of 100 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. (a) Write a differential equation for the amount of chemical in the pond at any time. Let q (t) denote the amount of chemical in the pond at time t. Use q as q (t). Do not use thousands separator in the answer field. (b) How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially?
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