A government program that currently costs taxpayers $$4\mathrm{.}5$ billion per year is cut back

by $6\%$ per year.

$($a$)$ Write an expression for the amount budgeted for this program after $n$ years.

$($b$)$ Compute the budgets for the first $4$ years.

$($c$)$ Determine the convergence or divergence of the sequence of reduced budgets. If

the sequence converges, find its limit$.$