kath and kim are a mother and daughter duo who share a joint instagram account. one day when they were sitting on a lowly 43 followers, they decided over a glass or 3 of yellowtail to make their profile public and gather followers. by posting pictures of their friend sharon, and kath’s husband powerwalking, they started seeing a successful growth in numbers.
at the end of the first week since becoming public (week 1), exactly half of their followers told one of their friends, who subsequently also became a follower. each week thereafter followed the same rate of increase.
which function below describes the relationship between the number of new followers (n) in a particular week, and the number of weeks that have elapsed since their profile became public (w, where w> 0)?