I was given some information:
An animal population grows by 8% every year, and in addition 40 individual move there at the end of each year. At the beginning of the first year the size of the population is 2000.
Determine a recursive sequence, which gives the number of individuals in the population at the beginning of the year n.
an= 1,08*an-1+40(from the previous year)
Then the exericise asks for the general equation for the population. By deriving the equation, I get
Yet the answer in the book states
And I don't know how they get it.
Any help is hugely appreciated, since I have a test soon, and currently am barely reaching the level required to pass.
Thank you in advance!