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?

Question

Mathematics

Belch

23 June, 17:34

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?

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Answers (1)

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Francesca Jacobson · Answer 1

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