Hi I'm stupid and don't into maths beyond like middle school. Help me find the pattern behind this series.

I'm using a program called synthedit that lets you create virtual instruments. The only part that's important here is that there's a slider that allows you to set how long each note is, but the slider isn't mapped to seconds and appears somewhat arbitrary. Probably based on the sample rate, or some binary/base 64 nonsense. Idk. Here's the data:

The numbers on the left are the numbers I inputted into the slider, next is how long that is in samples (441 samples = 1 second, not that it matters). Last is how much the length grew ie; what you have to multiply the last length by to get the current length.

1 = 000,000,154
2 = 000,000,322 - 2.09090909
3 = 000,000,726 - 2.25465839
4 = 000,001,792 - 2.46831956
5 = 000,004,454 - 2.48549107
6 = 000,011,113 - 2.49506062
7 = 000,027,868 - 2.50769369
8 = 000,069,936 - 2.509545
9 = 000,175,597 - 2.51082418
10 = 000,441,041 - 2.51166592

I want a function will tell me what value in the slider equals the length in samples that I want. The slider does accept decimal points ofc.

Let me know if you need more information.