A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be added to the tank at a certain rate, and the well-mixed solution will be drained from the tank at the same rate. The tank is considered “cleaned" when the dye concentration in the tank is no more than 0.001 grams/liter. (a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/ minute, how long does it take until the tank is clean? (b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured in?

A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be added to the tank at a certain rate, and the well-mixed solution will be drained from the tank at the same rate. The tank is considered “cleaned" when the dye concentration in the tank is no more than 0.001 grams/liter. (a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/ minute, how long does it take until the tank is clean? (b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured in?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will
be added to the tank at a certain rate, and the well-mixed solution will be drained from
the tank at the same rate. The tank is considered “cleaned" when the dye concentration
in the tank is no more than 0.001 grams/liter.
(a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/
minute, how long does it take until the tank is clean?
(b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured
in?

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