Question

EMERGENCY!!!! Each hour, every person who knows a rumor tells two other people. If one person starts the rumor, then after the first hour, three people know the rumor. The next hour, those three people each tell two more people. After eight hours, how many people will know the rumor? You do not have to include units in your answer. (I've asked this question before but the answers I got were 384 and 64 and they were both wrong)

Answer 1

After eight hours 6,561 people will know the rumor.

Explanation:

Since each hour, every person who knows a rumor tells two other people, so that if one person starts the rumor, then after the first hour, three people know the rumor, and the next hour, those three people each tell two more people, to determine after eight hours, how many people will know the rumor, the following calculation must be performed:

Hour 0 = 1

Hour 1 = 1 + 2 = 3

Hour 2 = 3 + 2 x 3 = 9

Hour 3 = 9 + 2 x 9 = 27

Hour 4 = 27 + 2 x 27 = 81

Hour 5 = 81 + 2 x 81 = 243

Hour 6 = 243 + 2 x 243 = 729

Hour 7 = 729 + 2 x 729 = 2,187

Hour 8 = 2,187 + 2 x 2,187 = 6,561

Therefore, after eight hours 6,561 people will know the rumor.