# Activity: Is Your Secret Safe? Think Exponentially

What you'll need:

- pen and paper
- a secret

1st: Think of a secret that you don't want anyone to know (aside from a couple of dear close friends).

2nd: Think of those close friends, draw them and write their names on each picture:

3rd: So, on the first day you tell each of your friends your secret, how many total people (aside from you) now know your secret? (Answer is 3, right?)

______ total people in ___ day

4th: Now, if the next day each of your friends tell three of their friends, how many people now know your secret (aside from you)? Draw them underneath each of their friends

______ total people in ___days

5th: Now, lets say the following day each of these friends tell three friends. Now how many people know your secret? Draw them

______ total people in ___ days

6th: We can see how fast your rumor can spread right? There's got to be a better way of calculating who will know your secret.

## In Walks Exponents ...

Exponents will quickly allow us to calculate how many people know your rumor

Day 1: 3^{1} (=3) know your secret

Day 2: 3^{2} (= 3×3 = 9) plus the original 3 know your secret

Day 3: 3^{3} (= 3×3×3 = 27) plus those on day 1 and day 2) know your secret

Day 4: 3^{4} (= 3×3×3×3 = 81) plus those on day 1,2 and 3) know your secret, and so forth...

As those who are told begin to tell others, the exponent grows.

Moral of the story? Keep your secrets with you, or those you really trust.

## Questions For You ...

- How long till your school or neighborhood knows your secret?

- How long till the whole country knows your secret?

- How long till the whole world knows your secret?

Activity courtesy of Hands On Math