Is there a way to find common formula for similar polynominals

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I'm trying to find a common formula for all the curves found in the attached chart. Is this possible at all

Chart

For instance, I have the first line, let's ignore the scale of the chart and use it as a grid, it has the following points:

  • P1 = x = 0 y = 90
  • P2 = x = 10 y = 102
  • P3 = x = 20 y = 112
  • P4 = x = 30 y = 119.5
  • P5 = x = 40 y = 124.5
  • P6 = x = 50 y = 128.5
  • P7 = x = 60 y = 130.5
  • P8 = x = 65 y = 131

Then there's another line, further up the chart, with the following points:

  • P1 = x = 0 y = 160
  • P2 = x = 10 y = 176
  • P2 = x = 10 y = 102
  • P3 = x = 20 y = 189.5
  • P4 = x = 30 y = 199.5
  • P5 = x = 40 y = 207
  • P6 = x = 50 y = 212
  • P7 = x = 60 y = 215
  • P8 = x = 65 y = 215.5

Is it possible to find the formula and apply it anywhere on the chart? I would appreciate your guidance and patience as I'm coming from a humanities education.