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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.

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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First-order differential equations are used to model word problems. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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