MATH 2163 Quiz: MATH 2163 OK State Quiz7
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Quiz # 2 math 2233, di erential equations sep. 4, 2008: a tank initially contains 200 gallons of salt water with a concentration of 2 oz/gal. Pure water ows into the tank at a rate of 10 gal/min, while the well-stirred mixture ows out of the tank at a rate of 5 gal/min. Find the total amount of salt in the tank after 10 minutes. Solution: let q(t) be the amount of salt in the tank at time t. then we have dq dt. = rate of salt in rate of salt out. And at time t = 0, we have the initial condition: Q(0) = 200 (gal) 2 (oz/gal) = 400 (oz) Combining them together gives the following initial value problem (ivp): ( dq dt = 1. To solve the ivp, we rst notice that the di erential equation is separable, 40 + t dt ln |q| = ln |40 + t| + c.
