Five children know a secret. Every day, the number of children who know the secret doubles. There are 1,280 children in the school. Of the secret continues to spread at this rate, how long will it take until all of the children in the school know the secret?

9 days

Step-by-step explanation:

Since the secret spread at a geometric rate we will use the geometric progression formulae

ar^n-1

First term = a = 5

common ratio is 2

For the nth term

5*2^n-1 = 1280 divide both sides of the equation with 5

2^n-1 = 256

2^n-1 = 2^8

n-1 = 8

n = 8+1

n=9

All the children will know the secret in 9 days

Alternatively

2nd day = 5*2^2-1

5*2^1=

5*2 = 10

3rd day = 20

4th day = 40

5th day = 80

6th day = 160

7th day = 320

8th day = 640

9th day = 1280 children