Question

You send a text to a friend. Your friend forwards it to 10 other friends, who each forward it to 10 more friends. The pattern continues for 5 rounds after your first text.

a. How many people will receive the text during the 4th round? Write your answer in scientific notation and in standard form.

b. How many total people have received the text? Write your answer in standard form. Explain your calculation.

Answer 1

a. The number of people that receive the text in the fourth round are 10³ people

b. The total number of people that receive the text are 1.1111 × 10⁴ people

Explanation:

a. The given information are;

The number of people the text is sent to in the first round = 1

In the second round, the number of people the text is sent to by people in the first round = 10

In the third round, the number people the text is sent to by the 10 people in the second round = 10 × 10 = 100 people = 10² people

In the fourth round, the number of people the text is sent to by the people in the third round = 100 × 10 = 1000 people = 10³ people

The number of people that receive the text in the fourth round = 10³ people

b. In the fifth round, the number of people, the people in the fourth round send the text to = 1000 × 10 = 10000 people = 10⁴ people

The total number of people that receive the text = 1 + 10 + 10² + 10³ + 10⁴ people = 11111 people = 1.1111 × 10⁴ people