Question

A certain rumor starts at a school with 1500 people in it. Originally just three people knew, but every day each person who knew told two other people. If the rumor continues to spread like this, how long will it take until the whole school knows?

Answer 1

Solve for the number of days
`d` such that

`3\cdot2^d = 1500`

`\implies 2^d = 500`

`\implies \log_2(2^d) = \log_2(500)`

`\implies d = \log_2(500) \approx \boxed{8.96578}`