On January 1st, Jerome concocts a rumor and tells Beth. On January 2nd, they each tell a new person. By the end of January 2nd, four people have heard the rumor. On each subsequent day, each person who has heard the rumor spreads it to a new person. How many people have heard the rumor by the end of January 8th?
By the end of January 3rd, there will be 8 people who have heard the rumor (4 original people + 4 new people).
By the end of January 4th, there will be 16 people who have heard the rumor (8 original people + 8 new people).
By the end of January 5th, there will be 32 people who have heard the rumor (16 original people + 16 new people).
By the end of January 6th, there will be 64 people who have heard the rumor (32 original people + 32 new people).
By the end of January 7th, there will be 128 people who have heard the rumor (64 original people + 64 new people).
By the end of January 8th, there will be 256 people who have heard the rumor (128 original people + 128 new people).