The amount of money that needs to be deposited into an account to reach some future goal is called the present value. The following table gives the present value (to the nearest dollar) for an account that earns 10% compounded annually so that the account value will be $50,000 after intervals ranging from 1 to 7 years.

Years                    Present value

1 ...............................  $45,455

2 ...............................    41,322

3 ...............................    37,566  

4 ...............................    34,151

5 ...............................    31,046

6 ...............................    28,224

7 ...............................    26,658

(a) Using x as the years and y as the present value, develop an exponential model for these data. Report the model to 4 significant digits.

(b) Use the model to find the present value (to the nearest dollar) of this account for its value to be $50,000 after 10 years.