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. there are how many people who have heard the rumor by the end of january 8th?

The rumor is spreading to a double amount of people each time and started with only one person.
On the first day, two people knew it. 2¹ = 2
On the second day, four people knew it. 2² = 4
On the third day, eight people knew it. 2³ = 8
On the nth day, the people that will know it = 2ⁿ
Thus, on the eighth day: 2⁸ = 256 people will know it

Yo no me sé esa mala mia