4. A village has an expected population growth rate (birth rate minus death rate) of \(r \%\) per year. In addition, \(N\) people are expected to move into the village each year. The expected population of the village is modelled by $$u _ { n + 1 } = 1.02 u _ { n } + 50$$ where \(u _ { n }\) is the expected population of the village \(n\) years from now.

1. State
   1. the value of \(r\),
   2. the value of \(N\). Given that the population 1 year from now is expected to be 560
2. solve the recurrence relation for \(u _ { n }\)
3. Hence determine, using algebra, the number of years from now when the model predicts that the population of the village will first be greater than 3000
   (Total for Question 4 is 10 marks)
   TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS END