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 8th, the number of people who have heard the rumor can be calculated as follows:
January 3rd: 8 people (4 from the previous day + 4 new people)
January 4th: 16 people
January 5th: 32 people
January 6th: 64 people
January 7th: 128 people
January 8th: 256 people
Therefore, by the end of January 8th, 256 people have heard the rumor.