In problems $1$ and $2,$ for part a$,$ solve the given recurrence equation using the iterative

method from class and in Example $10$ on page $168-169$ in the Rosen textbook. For part b$,$

define a recurrence equation and initial condition that represents the situation that is

described and then solve the recurrence equation using the same technique as in part a$.$

Show all of your work.$|$

a$.a_n=2a_{n-1}+3,a_0=1$

b$.$ At the beginning of year $1,$ the population of the country of Freedonia has $3075$

people. Each year, the population grows in two ways. One is through birth rates:

each year, the number of newborns is $6\%$ of the population at the beginning of the

year. The second way the population grows in through immigration: the country

allows exactly $35$ people into the country each year $($and that's how many actually

enter the country each year$).$ No one dies in Freedonia, and no one leaves. Write

and solve a recurrence equation $($with an initial condition$)$ that represents the

population of Freedonia at the beginning of year $n.($For the purposes of this

problem, we allow "fractional" people.$)$