Samantha took out a loan that does not require her to make any payments for 12​ months, although interest is being charged to her account. The table below shows the total amount she owes each month after taking the loan. Complete parts ​(a) through ​(f). Loan Balance
Month
0
1
2
3
4
Total Amount Owed​ ($)
​(a) Find an exponential model that is a reasonable fit for the data.
The exponential model that is a reasonable fit for the data is ​f(x)
3600 left parenthesis 1.019 right parenthesis Superscript x.
​(Type integers or decimals rounded to three decimal places as needed. Type an expression using x as the​ variable.)
​(b) How much will Samantha owe at the end of 12​ months, assuming she does not make any payments before​ then?
At the end of 12 months Samantha will owe ​$
nothing.
​(Round to the nearest integer as​ needed.)