5. \begin{figure}[h] \end{figure} The profit made by a company, \(\pounds P\) million, \(t\) years after the company started trading, is modelled by the equation $$P = \frac { 4 t - 1 } { 10 } + \frac { 3 } { 4 } \ln \left[ \frac { t + 1 } { ( 2 t + 1 ) ^ { 2 } } \right]$$ The graph of \(P\) against \(t\) is shown in Figure 2. According to the model,

1. show that exactly one year after it started trading, the company had made a loss of approximately £ 830000 A manager of the company wants to know the value of \(t\) for which \(P = 0\)
2. Show that this value of \(t\) occurs in the interval [6,7]
3. Show that the equation \(P = 0\) can be expressed in the form $$t = \frac { 1 } { 4 } + \frac { 15 } { 8 } \ln \left[ \frac { ( 2 t + 1 ) ^ { 2 } } { t + 1 } \right]$$
4. Using the iteration formula $$t _ { n + 1 } = \frac { 1 } { 4 } + \frac { 15 } { 8 } \ln \left[ \frac { \left( 2 t _ { n } + 1 \right) ^ { 2 } } { t _ { n } + 1 } \right] \text { with } t _ { 1 } = 6$$ find the value of \(t _ { 2 }\) and the value of \(t _ { 6 }\), giving your answers to 3 decimal places.
5. Hence find, according to the model, how many months it takes in total, from when the company started trading, for it to make a profit.
   (2)