6. 203 is the GOAT [2 points]Suppose that there are two goats on an island initially. Every year, the number of goats onthe island doubles, then some number of goats are added or removed (this addition/removalis specified in (a) and (b)).a) At the end of each year (after the goat population has doubled), an extra 100 goats areput on the island. Construct a recurrence relation for the number of goats on the islandat the start of thenth year. b) For the first four years, the goat population doubles with no addition/removal. From year5 on, at the end of yearn(after the goat population has doubled),ngoats are removed(so 5 goats are removed at the end of year 5, 6 goats at the end of year 6, etc.). Constructa recurrence relation for the number of goats on the island at the start of thenth year.