9. a series rc circuit has a battery of 12 volts connected in series to a resistor with resistance 100 k2 and a capacitor with capacitance 2 /f. there is an initial charge of 20 nc on the capacitor. the switch is thrown at t = 0 seconds. a) write the differential equation for the circuit. b) solve the equation to find q(t) and i(t).

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?