Question

Bobby posts an online video and sends it to three of his friends on a social media platform. After one minute passes, each of those friends shares the video with two of their friends. The process continues for a few minutes. Write a recursive process that represents the number of people who have received the video in n minutes

Answer 1

`f(n) = f(n- 1) * 2`;
`f(1) = 3`

Explanation:

Given

`1\ minute = 3\ friends`

Every other minute

`Each\ friend = 2\ other\ friends`

Required

Determine the recursive function

Let the number of minutes be represented with n.

The initial condition can be represented as:

`n = 1`

`f(1) = 3` --- i.e. 3 friends initially at the first minute

At every other minutes:

`n \ge 2` i.e 2 minutes upwards

This means that n follows the following sequence

`n \to n, n -1, n -2,n -3, n - 4,.....,4,3,2`

Note that the difference between each term is 1.

This means that recursive function has to be defined backwards i.e.

`f(n) = f(n- 1) * k`

Where k = 2

i.e. The number of friends that received the video from each friend

So, we have:

`f(n) = f(n- 1) * 2`

Hence, the recursive function is:

`f(n) = f(n- 1) * 2`;
`f(1) = 3`