The following table gives the value of an investment, after intervals ranging from 0 to 7 years, of $20,000 invested at 10%, compounded annually.
(a) Develop an exponential model for these data, accurate to four decimal places, with x in years and y in dollars.
(b) Use the model to find the amount to which $20,000 will grow in 30 years if it is invested at 10%, compounded annually.
Year ______________________ Amount Investment Grows To
0 ....................................................20,000
1 ....................................................22,000
2 ....................................................24,200
3 ....................................................26,620
4 ....................................................29,282
5 ................................................32,210.20
6 ................................................35,431.22
7 ................................................38,974.34