Question

A 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. dq/dt = grams/hour (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? q = Number grams The limiting amount (Click for List) depend on the amount that was present initially.

          A 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.

dq/dt = grams/hour

(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?

q = Number grams

The limiting amount (Click for List) depend on the amount that was present initially.

A 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.

dq/dt = grams/hour

(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?

q = Number grams

The limiting amount (Click for List) depend on the amount that was present initially.

Added by Eduardo B.

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