A chain email tells people to forward the email to 10 friends in order to have good luck. Assuming that everyone in the chain actually follows the directions, create a sequence to show how many people will get the email after 5 rounds of forwarding.(2 points)

Question

10, 100,
,
,
. .

Answer 1

To understand the email chain effect, we can analyze how many people receive the email after each round of forwarding.

1. Initial sender: 1 person (the original sender).
2. Round 1: Each person forwards the email to 10 friends. So:
   \(1 \times 10 = 10\) new recipients.
3. Round 2: Each of the 10 new recipients forwards it to 10 more friends:
   \(10 \times 10 = 100\) new recipients.
4. Round 3: Each of the 100 new recipients forwards it to 10 friends:
   \(100 \times 10 = 1,000\) new recipients.
5. Round 4: Each of the 1,000 new recipients forwards it to 10 friends:
   \(1,000 \times 10 = 10,000\) new recipients.
6. Round 5: Each of the 10,000 new recipients forwards it to 10 friends:
   \(10,000 \times 10 = 100,000\) new recipients.

So the sequence of people who will receive the email after each round is:

• Round 0 (original sender): 1
• Round 1: 10
• Round 2: 100
• Round 3: 1,000
• Round 4: 10,000
• Round 5: 100,000

The completed sequence after 5 rounds of forwarding is:

10, 100, 1,000, 10,000, 100,000.