- #1
davee123
- 672
- 4
Not sure if "General Math" is the best place for this, although I'm honestly not sure which sub-forum would be right.
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
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