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Question

Question
Marquan learns a new fact about his favorite animal, the sloth. He shares the fact with two other people. Those two people tell two others, and so on. How many people know the sloth fact after six rounds of information sharing?(1 point)
people

Answer 1

The information sharing follows a pattern where each person tells two others. Starting with Marquan, the number of people who know the fact can be calculated as follows:

1. Round 0 (Marquan): 1 person knows the fact.
2. Round 1: 1 (Marquan) tells 2 people. Total: 1 + 2 = 3.
3. Round 2: Each of the 2 people tells 2 others, so 2 × 2 = 4 new people learn the fact. Total: 3 + 4 = 7.
4. Round 3: Each of the 4 new people tells 2 others, so 4 × 2 = 8 new people learn the fact. Total: 7 + 8 = 15.
5. Round 4: Each of the 8 new people tells 2 others, so 8 × 2 = 16 new people learn the fact. Total: 15 + 16 = 31.
6. Round 5: Each of the 16 new people tells 2 others, so 16 × 2 = 32 new people learn the fact. Total: 31 + 32 = 63.
7. Round 6: Each of the 32 new people tells 2 others, so 32 × 2 = 64 new people learn the fact. Total: 63 + 64 = 127.

Therefore, after six rounds of information sharing, a total of 127 people know the sloth fact.