An important thing to practice is turning a real world problem into a mathematical model. Let's practice this with a bri

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An Important Thing To Practice Is Turning A Real World Problem Into A Mathematical Model Let S Practice This With A Bri 1 (79.86 KiB) Viewed 11 times

An important thing to practice is turning a real world problem into a mathematical model. Let's practice this with a brine mixing example. A tank holds 1000 litres of water in which 7000 grams of salt has been dissolved. Brine which contains 4 grams of salt per litre is run in at a rate of 10 litres per minute. (See below for a picture of the tank). The solution is thoroughly mixed and is extracted from the tank at the same rate. Let x be the number of grams of salt in the tank after t minutes. Based on the information given Initially there are • salt is being added to the tank at a rate of . the number of litres in the tank at time t is ● 100 differential equation grams of salt in the tank. The salt is evenly distributed in the tank by mixing. Hence if there are a grams of salt in the tank, then one litre taken from this tank contains grams of salt, and 10 X litres contains grams of salt. The change in salt with respect to time is described by the dx dt grams per minute = inflow - outflow 40 x 100