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I have coordinates of four points on a curve and want to find a function that will draw the curve.

The points are [0,0] [120,280] [240,2800] [360,28000]

It looks like an exponential curve in that 120 is 1/3 of 360 and 280 is 2.8 * 100, 240 is 2/3 of 360 and 2800 is 2.8 * 1000, 360 is 3/3 of 360 and 28000 is 2.8 * 10000

It looks like it should be a simple function. I tried the function finder on ZunZun but it produced hideously complicated functions that didn't output exact results.

Prajna Pranab
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1 Answers1

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The point $(0,0)$ is ruining your exponential. The other points fit $y=28\cdot 10^{x/120}$ perfectly. If the first point were $(0,28)$ it would fit as well. If you got your data off a graph, can you tell the difference between the two points?

Ross Millikan
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  • Fantastic Ross. Thank you. I still have some figuring out since I would like to get y = close to 0 when x is 0 but I guess that can't be so with this curve. – Prajna Pranab Nov 30 '19 at 17:44
  • On the scale of your data $28$ is close to $0$. – Ross Millikan Nov 30 '19 at 17:45
  • True. Thanks again Ross. – Prajna Pranab Nov 30 '19 at 17:48
  • I really can't say that without knowing about the source of the data. You may have some good reason to know that the curve should go through $(0,0)$. If the points are exact, I don't think you will get a nice fit. You could use $y=28\cdot (10^{x/120}-1)$, which misses all the others by $28$. Maybe that is more acceptable. – Ross Millikan Nov 30 '19 at 17:53
  • That's very helpful, Ross, thank you. Can I bias the curve so that it would also pass through (30,28) and as close as possible to (0,0)? – Prajna Pranab Nov 30 '19 at 18:48
  • If it helps I am using it to represent a life mapped around a circle where the first 120 degrees represents conception to birth, the next 120 degrees represents birth to 7.7 years and the final 120 degrees represents from 7.7 years to 77.7 years. The scale around the circle should give the age in days according to that exponential distribution. The 1st 120 degrees represents 280 days, by 7.7 years the age is approx 2800 days, by 77.7 years we reach approx 28000 days. – Prajna Pranab Nov 30 '19 at 19:01
  • The original curve goes through $(30,49.79)$ so with the subtraction of $28$ you are quite close. – Ross Millikan Nov 30 '19 at 19:19
  • Thanks Ross. I subtracted 28*(120-x)/119 where x < 120 and that achieved what I was looking for. – Prajna Pranab Dec 02 '19 at 14:10