- The number of visits to a website, in any particular month, is modelled as the number of visits received in the previous month plus \(k\) times the number of visits received in the month before that, where \(k\) is a positive constant.
Given that \(V _ { n }\) is the number of visits to the website in month \(n\),
- write down a general recurrence relation for \(V _ { n + 2 }\) in terms of \(V _ { n + 1 } , V _ { n }\) and \(k\).
For a particular website you are given that
- \(k = 0.24\)
- In month 1 , there were 65 visits to the website.
- In month 2 , there were 71 visits to the website.
- Show that
$$V _ { n } = 50 ( 1.2 ) ^ { n } - 25 ( - 0.2 ) ^ { n }$$
This model predicts that the number of visits to this website will exceed one million for the first time in month \(N\). - Find the value of \(N\).