Tank 1 in Figure 5 is filled with V₁ liters of water containing blue dye at an initial concentration of c₀ g/L. Water flows into the tank at a rate of R L/min, is mixed instantaneously with the dye solution, and flows out through the bottom at the same rate R. Let c₁(t) be the dye concentration in the tank at time t.

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dc₁ (a) Explain why c₁ satisfies the differential equation dt (b) Solve for c₁ (t) with V₁ = 300 L, R = 50, and co = 10 g/L. 3 R V₁ R(L/min) 0 Tank 1 R (L/min) -C1. Tank 2 R (L/min)