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I have a dataset like the following...

1 : 3325 
10 : 3301
100 : 3068 
500 : 2215 
1000 : 1526 
5000 : 424 
10000 : 266 
100000 : 45 
200000 : 25 
500000 : 7

Just from the look of the numbers it appears to be a curve with 3325 being the highest point on the left if you plotted it on a chart and 7 being the furthest on the bottom right of the chart.

My question is knowing these numbers. How can I calculate a number on that curve in between. Lets say instead of getting the result for 1 or 10 or 100, what would the result be for let's say 55 or 7433?

I am basically trying to create a function in code to take in this dataset and then allow me to find the points in between. A straight line between each point would be easy but a curve would be more accurate.

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    Have you considered piecewise cubic Hermitian interpolation (PCHIP)? For example, http://orion.math.iastate.edu/docs/cmlib/pchips.html – 2017-01-19
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    Cubic spline approximation is maybe simpler. For example, if you use Matlab, here is a good presentation:(http://people.whitman.edu/~hundledr/courses/M467/CubicSplines.pdf) – 2017-01-19

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