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Differential EquationsMediumNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Medium problem

A tank holds 100100 L of brine (volume held constant by equal in/out flow) with 5050 kg of salt dissolved. Fresh water flushes the tank so the salt amount obeys S′=−120SS' = -\dfrac{1}{20}S (S in kg, t in minutes), S(0)=50S(0) = 50. Using Euler's method with h=4h = 4 minutes for two steps, estimate the salt concentration (in kg/L) at t=8t = 8 minutes. Express your answer as a common fraction.