+ (a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwater enters the tank at a rate of 4 liters per minute, and the well-mixed solution leaves the tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tank at time t (in minutes). Set up and solve a differential equation to find y(t). [Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixed solution, so the total volume of the saltwater in the tank (100 liters) remains constant over time. At any time (t), the salt content (concentration) in the tank is y(t) (kg/liter)] 100 (b) How much time does it take for the salt content to decrease by 50%. [Note: Write down the numerical expression, no need to use calculator]
+ (a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwater enters the tank at a rate of 4 liters per minute, and the well-mixed solution leaves the tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tank at time t (in minutes). Set up and solve a differential equation to find y(t). [Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixed solution, so the total volume of the saltwater in the tank (100 liters) remains constant over time. At any time (t), the salt content (concentration) in the tank is y(t) (kg/liter)] 100 (b) How much time does it take for the salt content to decrease by 50%. [Note: Write down the numerical expression, no need to use calculator]
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
![+
(a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwater
enters the tank at a rate of 4 liters per minute, and the well-mixed solution leaves
the tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tank
at time t (in minutes). Set up and solve a differential equation to find y(t).
[Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixed
solution, so the total volume of the saltwater in the tank (100 liters) remains
constant over time. At any time (t), the salt content (concentration) in the tank is
y(t) (kg/liter)]
100
(b) How much time does it take for the salt content to decrease by 50%.
[Note: Write down the numerical expression, no need to use calculator]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe95c0ed5-6562-4de3-90f0-5232d13c65eb%2Faa19dbb7-962c-4f8a-9c4b-e7a62ab95c2d%2F7z2j85l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:+
(a) A tank contains 100 liters of saltwater with 5 kg of dissolved salt. Freshwater
enters the tank at a rate of 4 liters per minute, and the well-mixed solution leaves
the tank at the same rate. Let y(t) represent the amount of salt (in kg) in the tank
at time t (in minutes). Set up and solve a differential equation to find y(t).
[Hint: The inflow rate of fresh water equals to the outflow rate of the well-mixed
solution, so the total volume of the saltwater in the tank (100 liters) remains
constant over time. At any time (t), the salt content (concentration) in the tank is
y(t) (kg/liter)]
100
(b) How much time does it take for the salt content to decrease by 50%.
[Note: Write down the numerical expression, no need to use calculator]
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