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To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modeled by the function C(t) = 401 160+t , where C is the concentration, in grams per liter, and t is the time, in minutes. a) In how many minutes the saline concentration will be 15 g/L? b) Is there an upper limit to the concentration in the tank? Explain. c) What restrictions must be placed on the domain of C if the tank has a maximum capacity of 150 000 L?

To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modeled by the function C(t) = 401 160+t , where C is the concentration, in grams per liter, and t is the time, in minutes. a) In how many minutes the saline concentration will be 15 g/L? b) Is there an upper limit to the concentration in the tank? Explain. c) What restrictions must be placed on the domain of C if the tank has a maximum capacity of 150 000 L?

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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To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modeled by the function C(t) = 40t 160+t , where C is the concentration, in %3D grams per liter, and t is the time, in minutes. a) In concentration will be 15 g/L? b) Is there an upper limit to the concentration in the tank? Explain. how many minutes the saline c) What restrictions must be placed on the domain of C if the tank has a maximum capacity of 150 000 L?
Transcribed Image Text:To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500 L/min to a tank of water that initially contained 8000 L of pure water. The resulting concentration of the solution in the tank can be modeled by the function C(t) = 40t 160+t , where C is the concentration, in %3D grams per liter, and t is the time, in minutes. a) In concentration will be 15 g/L? b) Is there an upper limit to the concentration in the tank? Explain. how many minutes the saline c) What restrictions must be placed on the domain of C if the tank has a maximum capacity of 150 000 L?
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