Homer enters the visitors’ chambers, and his geiger-beeper goes off. He shuts off the beep, removes the device from his shoulder patch and holds it near the only new object in the room: an orb which is to be presented as a gift from the visiting Cartesians. Pushing a button marked “monitor”, Homer reads that the orb is a radioactive source with a counting rate of 4000 counts/s. After 10 min, the counting rate has dropped to 1000 counts/s. The source’s half-life appears on the geiger-beeper display.

(a) What is the half-life?

(b) What will the counting rate be 20 min after the monitoring device was switched on?