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Problem 5. Suppose a large tank contains 20L of pure water, into which 10 grams of lactose is dissolved. At exactly noon, a solution containing 3.5 g/L of lactose is pumped into the tank at a rate of 4 L/min. At the same time, a valve is opened in the bottom of the tank, allowing the well-mixed solution to flow out at a slower rate of 1 L/min. The tank has a total capacity of 100L. (a) Set up and solve an initial value problem to find the amount of lactose (in grams) contained within the tank t minutes after noon. (b) Use your system to answer the following question: Which of the following two events will occur first? • The tank will overflow. • The solution in the tank will reach a concentration of at least 3 g/L of lactose. Completely justify your answer by setting up and solving an initial value problem. Make sure your answer indicates the exact times at which the two events occur (if ever).

Problem 5. Suppose a large tank contains 20L of pure water, into which 10 grams of lactose is dissolved. At exactly noon, a solution containing 3.5 g/L of lactose is pumped into the tank at a rate of 4 L/min. At the same time, a valve is opened in the bottom of the tank, allowing the well-mixed solution to flow out at a slower rate of 1 L/min. The tank has a total capacity of 100L. (a) Set up and solve an initial value problem to find the amount of lactose (in grams) contained within the tank t minutes after noon. (b) Use your system to answer the following question: Which of the following two events will occur first? • The tank will overflow. • The solution in the tank will reach a concentration of at least 3 g/L of lactose. Completely justify your answer by setting up and solving an initial value problem. Make sure your answer indicates the exact times at which the two events occur (if ever).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 5. Suppose a large tank contains 20L of pure water, into which 10 grams of lactose is dissolved. At exactly noon, a solution containing 3.5 g/L of lactose is pumped into the tank at a rate of 4 L/min. At the same time, a valve is opened in the bottom of the tank, allowing the well-mixed solution to flow out at a slower rate of 1 L/min. The tank has a total capacity of 100L. (a) Set up and solve an initial value problem to find the amount of lactose (in grams) contained within the tank t minutes after noon. (b) Use your system to answer the following question: Which of the following two events will occur first? • The tank will overflow. • The solution in the tank will reach a concentration of at least 3 g/L of lactose. Completely justify your answer by setting up and solving an initial value problem. Make sure your answer indicates the exact times at which the two events occur (if ever).
Transcribed Image Text:Problem 5. Suppose a large tank contains 20L of pure water, into which 10 grams of lactose is dissolved. At exactly noon, a solution containing 3.5 g/L of lactose is pumped into the tank at a rate of 4 L/min. At the same time, a valve is opened in the bottom of the tank, allowing the well-mixed solution to flow out at a slower rate of 1 L/min. The tank has a total capacity of 100L. (a) Set up and solve an initial value problem to find the amount of lactose (in grams) contained within the tank t minutes after noon. (b) Use your system to answer the following question: Which of the following two events will occur first? • The tank will overflow. • The solution in the tank will reach a concentration of at least 3 g/L of lactose. Completely justify your answer by setting up and solving an initial value problem. Make sure your answer indicates the exact times at which the two events occur (if ever).
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