A stirred tank initially has 500 L brine at 200 g/L. Feed at 100 g/L enters at 15 L/min and an equal fully mixed flow leaves. The equation is $dC/dt+.03C=3$. Find C after 1.5 hours, in g/L, to two decimals.
Constant volume and complete mixing give equilibrium concentration $C_\infty=3/.03=100$ g/L. Solve the linear ODE with $C(0)=200$: $C(t)=100+100e^{-.03t}$. Convert 1.5 hours to 90 minutes, so $C(90)=100+100e^{-2.7}=106.72055\ldots$. Answer **106.72 g/L**.
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