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2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000 gal of water, while Pond B holds 200, 000 gal of water. The fresh water stream flows through these ponds at a rate of 1000 gal/hr. Assume that at some time, say t = 0, 1000 lb of a toxin is spilled into Pond A and disperses rapidly enough that a well-stirred assumption is reasonable. (a) Let QA(t) and QB(t) represent the quantity of toxin in Ponds A and B, respectively, at time t. Write down the initial value problems that indicate how the quantity of toxin in each pond varies with time. (b) Solve the initial value problems. (c) What is the maximum quantity of toxin present in Pond B and at what time after the spill is this maximum value reached? (d) How much time must elapse before the concentration of toxin in both ponds has been reduced to 1 lb per million gallons?

2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000 gal of water, while Pond B holds 200, 000 gal of water. The fresh water stream flows through these ponds at a rate of 1000 gal/hr. Assume that at some time, say t = 0, 1000 lb of a toxin is spilled into Pond A and disperses rapidly enough that a well-stirred assumption is reasonable. (a) Let QA(t) and QB(t) represent the quantity of toxin in Ponds A and B, respectively, at time t. Write down the initial value problems that indicate how the quantity of toxin in each pond varies with time. (b) Solve the initial value problems. (c) What is the maximum quantity of toxin present in Pond B and at what time after the spill is this maximum value reached? (d) How much time must elapse before the concentration of toxin in both ponds has been reduced to 1 lb per million gallons?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000 gal of water, while Pond B holds 200, 000 gal of water. The fresh water stream flows through these ponds at a rate of 1000 gal/hr. Assume that at some time, say t = 0, 1000 lb of a toxin is spilled into Pond A and disperses rapidly enough that a well-stirred assumption is reasonable. (a) Let Qa(t) and Q(t) represent the quantity of toxin in Ponds A and B, respectively, at time t. Write down the initial value problems that indicate how the quantity of toxin in each pond varies with time. (b) Solve the initial value problems. (c) What is the maximum quantity of toxin present in Pond B and at what time after the spill is this maximum value reached? (d) How much time must elapse before the concentration of toxin in both ponds has been reduced to 1 lb per million gallons?
Transcribed Image Text:2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000 gal of water, while Pond B holds 200, 000 gal of water. The fresh water stream flows through these ponds at a rate of 1000 gal/hr. Assume that at some time, say t = 0, 1000 lb of a toxin is spilled into Pond A and disperses rapidly enough that a well-stirred assumption is reasonable. (a) Let Qa(t) and Q(t) represent the quantity of toxin in Ponds A and B, respectively, at time t. Write down the initial value problems that indicate how the quantity of toxin in each pond varies with time. (b) Solve the initial value problems. (c) What is the maximum quantity of toxin present in Pond B and at what time after the spill is this maximum value reached? (d) How much time must elapse before the concentration of toxin in both ponds has been reduced to 1 lb per million gallons?
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