Problem Set No. 2
Application of First-Order Ordinary Differential Equations
1. A tank contains 2,000 gallons of brine. Brine containing 5 lb/gallon
of salt flows in at a rate of 10 gallon/minute. The mixture kept
uniform by stirring, flows out at a rate of 20 gallon/minute. If the
concentration of the salt is 8 lb/gallon at the end of 1 hour, how
much was the concentration of the salt at the beginning?
2. At 12:00 noon a thermometer reading 60C is taken outside where
the air temperature is 24C. At 12:02 PM the reading is 89.6F. Later
the thermometer is brought inside where the temperature is 60C.
At 12:10 PM, the reading is 58.24C. When was the thermometer
brought inside?
3. A bacteria culture is known to grow at a rate proportional to the
amount present. After one hour, 1000 strands of the bacteria are
observed in the culture; after four hours, 3000 strands. How many
strands will there be after 5 hours?
4. An RC circuit has an emf of 10 sin t (volts), a resistance of 100 ohms,
a capacitance of 0.005 farad, and no initial charge on the capacitor.
Find the current in the circuit at any time t.
5. An RL circuit has a resistance of 10 ohms, an inductance of 1.5
henries, an applied emf of 9 volts, and an initial current of 6 amperes.
Find the current in the circuit at any time t.