You make one charge to a new credit card, but then charge nothing else and make the minimum payment each month. You can't find all the statements, but the accompany table shows, for those that you do have, your balance $B,$ in dollars, after you make $n$ payments.

$\backslash$table$[[$Payment $n,2,4,7,11],[$Balance$,430\mathrm{.}82,363\mathrm{.}93,282\mathrm{.}56,201\mathrm{.}63]]$

$($a$)$ Use regression to find an exponential model for the data in the table. Round the decay factor to four decimal places.

$B=510*{0\mathrm{.}9191}^n$

$($b$)$ What was the initial charge?

$$510$

$($c$)$ When will you pay off this balance? Round to the nearest whole month.