question archive Lucas's friend Isabel is performing in a singing competition
Lucas's friend Isabel is performing in a singing competition
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Lucas's friend Isabel is performing in a singing competition. The winner of the competition will be determined by call-in votes. To help Isabel earn votes, Lucas sends text messages to 8 of his friends. He then asks each of his friends to send texts to 8 more friends, and asks his friends to ask each of their friends to send 8 texts. He is hoping for this pattern to continue and that many people will receive text messages telling them to vote for Isabel. Call each set of text messages a "round" of text messages, where Lucas's messages are the first round, Lucas's friends messages are the second round, and so on. Assuming that no one sends texts to the same person, how many texts will be sent after x rounds of text messages?
What would a diagram look like modeling the first few rounds of the situation?
How many texts were sent the first round?
How many texts were sent the first round?
Determine algebraically how many texts were sent in rounds 3, 4, and 5.
What would a table showing the number of texts after the first five rounds? (Let x represent the number of rounds, and y represent the number of texts)
If you know the number of texts sent in round x-1, how many texts will be sent in round x?
How many texts will be sent in round x? In other words, what is the explicit definition (algebraic expression) of the number of texts sent in any round, x?
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Answer:
1. The diagram is given below in the explanation.
2. In the first round 8 texts were sent.
3. In the first round 8 texts were sent.
4. The number of texts sent in 3rd , 4th and 5th rounds are 512, 4096 and 32768.
5. Table is given below.
6. To find the number of text sent in the x the round, multiply the number of text sent in the x-1th round by 8.
7. The number of texts sent in the xth round is given by 8x.
Now the first person send text to 8 friends and ask them to forward to text to next 8 friends so the diagram will be as follow:
In the first round Lucas sends the text to 8 people.
Now in the second round 8 people will send text to 8 people each, that is, 8*8 = 64 peoples.
In the third round these 64 people will send text to 8 people each, that is, 64*8 = 512 peoples.
In the fourth round these 512 people will send text to 8 people each, that is, 512*8 = 4096 peoples.
In the fifth round these 4096 people will send text to 8 people each, that is, 4096*8 = 32768 peoples.
The table showing the number of texts after the 5th round is as follows:
If we know the number of the texts sent in x-1th round then the number of texts sent in the x th round will be 8 times the number of text sent in the x-1th round.
The number of text sent in the x the round = 8x.
PFA
