# Modeling with first order Differential Equations (Five Problems).

9. When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t). where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity Jo of the incident beam. What is the intensity of the beam 15 feet below the surface?

19. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing I gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

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20. Solve Problem 19 assuming that pure water is pumped into the tank.

29. A 100-volt electromotive force is applied to an RC series circuit in which the resistance is 200 ohms and the capacitance is 10^-4 farad. Find the charge q(t) on the capacitor if q(0)=0. Find the current i(t).

30. A 200-volt electromotive force is applied to an RC series circuit in which the resistance is 1000 ohms and the capacitance is 5 X 10^-6 farad. Find the charge q(t) on the capacitor if q(0)=0. Find the current i(t).

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