a. Explanation Given information: At t = 0 , a tank of volume 300 litres is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exists at the same rate. Let c 1 ( t ) be the salt concentration at time t. Calculation: Let y ( t ) be the amount of salt in the tank at time t, then c 1 ( t ) = y ( t ) 100 . Then the rate of change of amount of salt in the tank is d y d t = salt rate in – salt rate out = ( 40 L/min ) ( 0 g/L ) − ( 40 L/min ) ( y ( t ) 100 g/L ) = 0 − 2 y ( t ) 5 = − 2</ b. To determine To solve: The salt concentration c 1 ( t ) in the tank as a function of time.

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 10, Problem 45CRE

To determine

To find:A differential equation satisfied by c1(t) .

To determine

To solve:The salt concentration c1(t) in the tank as a function of time.

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Chapter 10, Problem 44CRE

Chapter 10, Problem 46CRE

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A differential equation satisfied by c 1 ( t ) .

Solution Summary: The author explains how to find a differential equation satisfied by c_1(t).