3. A rumour is being spread in a community that the president is going to retire before the next election 2015. Initially 2 peop
le were told the rumour and each of these people told 2 others the following day. Each of the 2 people told by the initial people told 2 others the day after they were told. If this process keeps up, how many people will be told the rumour on the fifth day?
You start with 2 people on day 1. On day 2 each one of them tells 2 other people, which means 4 new people are told the rumor. We can use the formula p(d)= n + n^n + n^(n+1) + n^(n+2).... d times, where p(d) is the number of people told the rumor on the day d, n being the Number of people told by each person every day, as well as the initial people. So the formula is
