1. An area of woodland contains a mixture of blue and yellow flowers.

A study found that the proportion, \(x\), of blue flowers in the woodland area satisfies the differential equation $$\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { x t ( 0.8 - x ) } { x ^ { 2 } + 5 t } \quad t > 0$$ where \(t\) is the number of years since the start of the study.
Given that exactly 3 years after the start of the study half of the flowers in the woodland area were blue,

1. use one application of the approximation formula \(\left( \frac { \mathrm { d } y } { \mathrm {~d} x } \right) _ { n } \approx \frac { y _ { n + 1 } - y _ { n } } { h }\) to estimate the proportion of blue flowers in the woodland area half a year later.
2. Deduce from the differential equation the proportion of flowers that will be blue in the long term.