A tank contains 225 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t) is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation dy dt = 2 − 3y 225 + 2t. Solve this equation and find the concentration after 20 minutes. (Round your answer to four decimal places.)
A tank contains 225 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t) is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation dy dt = 2 − 3y 225 + 2t. Solve this equation and find the concentration after 20 minutes. (Round your answer to four decimal places.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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A tank contains 225 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If
y(t)
is the amount of salt (in kilograms) after t minutes, show that y satisfies the
dy |
dt |
3y |
225 + 2t |
Solve this equation and find the concentration after 20 minutes. (Round your answer to four decimal places.)
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