The process of sharing information can be modeled as a geometric sequence. Marquan starts with 1 person (himself), and each round, every person shares the fact with 2 others.
- Round 0: 1 person (Marquan)
- Round 1: 2 people (Marquan shares with 2 others)
- Round 2: 4 people (each of the 2 people from Round 1 shares with 2 others)
- Round 3: 8 people (each of the 4 people from Round 2 shares with 2 others)
- Round 4: 16 people (each of the 8 people from Round 3 shares with 2 others)
- Round 5: 32 people (each of the 16 people from Round 4 shares with 2 others)
- Round 6: 64 people (each of the 32 people from Round 5 shares with 2 others)
At each round \( n \), the number of new people who learn the fact is \( 2^n \).
So after 6 rounds of sharing, the total number of people who know the fact is:
- Round 0: \( 1 = 2^0 \)
- Round 1: \( 2 = 2^1 \)
- Round 2: \( 4 = 2^2 \)
- Round 3: \( 8 = 2^3 \)
- Round 4: \( 16 = 2^4 \)
- Round 5: \( 32 = 2^5 \)
- Round 6: \( 64 = 2^6 \)
To find the total number of people who know the fact after six rounds, we sum all the people from each round:
\[ 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 \]
Thus, after six rounds of information sharing, the total number of people who know the sloth fact is 127.