3. A tank is lled with 8 gal of brine in which 2 lb of salt is dissolved. Brine having 3 lb of salt per gallon enters the tank at 4 gal per minute, and the well-stirred mixture leaves at the same rate. (a) Set up a differential equation for the amount of salt in the tank at time t. (b) Find the amount of salt as a function if time. (c) Find the concentration of salt in the tank after 8 min. .r (d) How much salt is in the tank after a very long time? Answers: (h) 24 22e_5 (c} ~ 3 Ila/gal 4. Chemical A is transformed into chemical B. The rate at which B is formed varies directly as the amount ofA present at any instant. If 10 lb of A is present initially and if 3 Ibis transformed into B in 1 hour: (a) How much of A is transformed after 2, 3, and 4 hours. (b) In what time is 75% of chemical A transformed? Answers: (a) 5.1 lb, 6.6 lb, 7.6 lb (b) 3 hr 53 min. 9. A 402 resistor and an inductor of 1 henry are connected in series with an emf of 100e * cos(50t), t 2 0. Find I(t) if I = 0 at t = 0. [E =VR+L-_ dt Answer: I(t) = 2e -sin(50t)10. A capacitor of 5 x10_3 farads is in series with a 250 resistor and an emf of 50 volts. The switch is closed at t = 0. Assuming that the charge on the capacitor and the current are zero at t = 0, find: (a) the charge at any time t (b) the current at any time t [Kirchoff's law for series circuits with an emf (E), a resistor (R), and a capacitor (c) is: E = VR + VC, where VR=IR,VC=%,I=% 1-98! \"'9 8: b I==2 4 I l d: e Answers: (a) Q =