week_03_3.1,3.3 - MATH2860U: Chapter 3 1 MODELLING WITH...

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MATH2860U: Chapter 3 1 MODELLING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS Linear Models (Section 3.1 of Zill and Cullen, pg. 83) Recall: Earlier, we discussed the process of setting up linear models. We also discussed how to solve linear differential equations. Let’s put all of this together and solve some linear DEs arising in applications. Application: A 2000L tank contains 70 L of water with 0.3 kg/L of dissolved salt. Water containing 0.1 kg of salt per litre enters the tank at a rate of 8 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 6 L/min. How much salt will be in the tank after 5 min?
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MATH2860U: Chapter 3 2 Application: A radioactive substance decays at a rate proportional to the amount present, and half the original quantity is left after 1500 years. If the original quantity is Q 0 , how much remains after 2000 years? [Source: Elementary Differential Equations with Boundary Value Problems by William F. Trench] Application: A 7-volt battery is connected to a series circuit in which the inductance is 2
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week_03_3.1,3.3 - MATH2860U: Chapter 3 1 MODELLING WITH...

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