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A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.4 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.02 kg/L? Determine the mass of salt in the tank after t min. mass = kg When will the concentration of salt in the tank reach 0.02 kg/L? The concentration of salt in the tank will reach 0.02 kg/L after (Round to two decimal places as needed.) minutes.

A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.4 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.02 kg/L? Determine the mass of salt in the tank after t min. mass = kg When will the concentration of salt in the tank reach 0.02 kg/L? The concentration of salt in the tank will reach 0.02 kg/L after (Round to two decimal places as needed.) minutes.

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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A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.4 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.02 kg/L? Determine the mass of salt in the tank after t min. mass= kg When will the concentration of salt in the tank reach 0.02 kg/L? The concentration of salt in the tank will reach 0.02 kg/L after (Round to two decimal places as needed.) minutes.
Transcribed Image Text:A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.4 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.02 kg/L? Determine the mass of salt in the tank after t min. mass= kg When will the concentration of salt in the tank reach 0.02 kg/L? The concentration of salt in the tank will reach 0.02 kg/L after (Round to two decimal places as needed.) minutes.
The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 5/yr. However, commercial fishing removes fish mass at a constant rate of 17 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? When will all the fish be gone? The fish will all be gone in years. (Round to three decimal places as needed.) If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? For the mass of fish to remain constant, commercial fishing must remove fish at a constant rate of (Round to the nearest whole number as needed.) million tons per year.
Transcribed Image Text:The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 5/yr. However, commercial fishing removes fish mass at a constant rate of 17 million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? When will all the fish be gone? The fish will all be gone in years. (Round to three decimal places as needed.) If the fishing rate is changed so that the mass of fish remains constant, what should that rate be? For the mass of fish to remain constant, commercial fishing must remove fish at a constant rate of (Round to the nearest whole number as needed.) million tons per year.
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Step 1

We have to form a differential equation for amount of salt after t minutes then solve it using initial value to get amount . 

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