SOLVE ASAP PLZ AND EXPLAIN STEPS SHOW CODE I WANT FO UNDERSTAND A discrete dynamical system, $a(n+1)=ra(n)+b{s}^n,$ can be solved by the following:

$a(n)=c{r}^n+\frac{b}{s-r}{s}^n,ifrs$

or$,$

$a(n)=c{r}^n+\frac{bn}{r}{s}^n,ifr=s$

You have already solved a problem in SYST $220$ where you used difference equation given above for calculating the yearly account balance in a bank account with the following data:

$8\%$ interest rate compounded annually

Annual deposits at the end of each year with an increase of $5\%$ each year. The first deposit is $$100($at the end of first year$)$

No initial balance, $a(0)=0$

The following would be the difference equation modeling the system:

$a(n+1)=1\mathrm{.}08a(n)+100(1\mathrm{.}05{)}^n,a(0)=0$

$($a$)$ Construct a MATLAB function calculate$\_$balance$(n),$ that returns the account balance at the end of $n$ years.

$($b$)$ Calculate the account balance at the end of $2nd,5$ th$,$ and $10$ th years $($ie$.,n=2,5,10)$ using the function in Part

$($a$)$ and output using fprintf.

All your calculations should be provided in MATLAB.