Solve Mixing Problems: Differential Equation Modeling

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The discussion centers on modeling a mixing problem using differential equations, specifically for a tank containing 1920 L of pure water into which a sugar solution enters at a rate of 7 L/min. The correct formulation of the differential equation is S'(t) = 0.49 - (7S/1920), where S represents the amount of sugar in kilograms at time t. A common error identified is the miscalculation of the sugar influx rate, where 0.07 kg/L multiplied by 7 L/min equals 0.49 kg/min, not 0.049 kg/min. This highlights the importance of precise arithmetic in formulating differential equations.

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A tank contains 1920 L of pure water. A solution that contains .07 kg of sugar per liter enters tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate. With S representing the amount of sugar (in kg) at time t (in minutes) write a differential equation which models this situation.

S'(t)=r1c1-r2c2
r1=r2=7
c1=.07kg
c2=S(t)/V(t)=S/1920

so wouldn't [tex]S'(t)=.049- \frac{7S}{1920}[/tex]

I'm not sure why this is wrong
 
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Would you believe arithmetic? 0.07*7= 0.49, not 0.049!
 

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