So, I've got a data set. It looks like it's a standard exponential curve, but I honestly don't remember how to figure out an equation that will approximate it well. Actually, I guess I DO remember how to do an Nth degree polynomial given N data points, but I don't trust the standard polynomial form to do the job here, since I want to predict the data set a ways out.

The 125 data points I have currently are:

33.67

36.8

39.6

50.92

52.8

54.72

55.2

64.68

72.52

76.72

85.47

87.2

99.96

106.78

123.2

132

145.36

147.2

166.1

175.95

204.37

212.38

226.6

230.42

271.22

283.08

315.1

358.6

391.6

416.9

440

461.1

532.4

565.8

622.4

652

697.23

789.95

813.78

832

912

957.84

1155.08

1255.8

1277.3

1474

1601.3

1676.22

1782.73

2034.12

2097.6

2307.24

2647.84

2683.64

2964

3402.6

3622.6

4040.4

4296.4

4605.3

4803.5

5863.7

6259

6509

7378.4

7711.2

8432

8903

9694.2

10488

11144.1

12198

13727

14739.2

16148.2

18921

20608.9

21128

21660

25281

26319.7

30084

32050.8

32554.2

35431.2 <=== It's possible that somewhere around here, the function changes!

36432

40404

40510.2

44484

47424

51604

55624

61759

66670

72228

78880

85042

94242

100080

111240

121040

129456

139840

152613

171600

181440

197776

215644

233280

258750

279900

302820

328510

357280

388750

429000

462300

506350

535300

590400

638400

701800

753960

810250

980900

I'd like to be able to approximate the next 50 or so points (the next 47 to be precise). I've tried playing around with the basics of e^Ax+B or x^A+B, but these don't seem to give me the right curve. Also, there may be TWO growth formulas, I'm not sure. The first two-thirds or so might follow one pattern, and the latter one-third or so might follow another pattern. So really, I'm more interested in the latter one-third, in the event that there really ARE two different formulas.

Ideas anyone on how to go about approximating this? Is my best bet really to do some crazy 40th order polynomial (I sure hope not)?

DaveE