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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?

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So we want to know how many people have heard the rumor if the rumor started on january 1st and has spread exponentially, 2^n, where n>0 and a whole number and the rumor was spreading till january 8th. So on the january 1st 2 people knew the rumor and the rumor was spreading for 8 days. That means we have 2^n people who know the rumor where 2 is the number of people each person tells the rumor and 8 is the number of days the rumor was spreading. so 2^8 is 256. So 256 people heard the rumor.
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