How to calculate an exponential relationship between percentages?

Question

I have several data points from which I'm trying to calculate a formula:

• Column 1 ("I") is a number (inclusively) between 0 and column 2.
• Column 2 ("C") is a fixed value in each case.
• Column 3 ("R") is the ratio I / C
• Column 4 ("P") is what I'm trying to find out.
• Both column 3 ("R") and column 4 ("P") will always fall in the range 0 to 1 and can therefore be expressed as percentages.

 0 | 16 | 0.000 | 1.000
 1 | 16 | 0.063 | 0.518
 2 | 16 | 0.125 | 0.268
 3 | 16 | 0.188 | 0.139
 4 | 16 | 0.250 | 0.072
 5 | 16 | 0.313 | 0.037
 6 | 16 | 0.375 | 0.019
 7 | 16 | 0.438 | 0.010
 8 | 16 | 0.500 | 0.005
 9 | 16 | 0.563 | 0.003
10 | 16 | 0.625 | 0.001
11 | 16 | 0.688 | 0.001
12 | 16 | 0.750 | 0.000
13 | 16 | 0.813 | 0.000
14 | 16 | 0.875 | 0.000
15 | 16 | 0.938 | 0.000
16 | 16 | 1.000 | 0.000

The data above is limited to 3 decimal places. I can see that the relationship is exponential in nature, but I don't know exactly what the relationship is.

Is there a process that I can use to determine the formula based on these data points?

EDIT: When graphed out, I believe the above data points form a logarithmic graph.

Answer 1

Choosing an exponential model, the best fit would be $$P=0.98\cdot e^{-0.65348I}=0.98\cdot0.52^I$$ with a remarkable correlation of $0.98$.