Question

A community organizes a phone tree in order to alert each family of emergencies. In the first stage, one person calls five families. In the second stage, each of the five families calls another five families, and so on. How many stages need to be reached before 19,530 families or more have been called?

Answer 1

Answer: It will take 7 stages for all 19,530 families to be called.

In the first stage, only 5 families are called.

In the second stage, we would have 5 x 5 = 25 families being called.

In the third stage, we would have 5 x 5 x 5 = 125 families being called.
We can use exponents to finish the list and see when our goal is reached.

4th stage: 5^4 = 625

5th stage: 5^5 = 3125

6th stage: 5^6 = 15625

7th stage: 5^7 = 78,125