Reverse engineer simple curved growth between 2 values

Question

This is probably super basic, but I'm not very good at this stuff so I'm trying it here :)

I have some values that I know the plot values of, but need the actual formula to determine future values dynamically in my programming code.

I have the following 2 axis that I have the stepping values of, and can redraw them in RStudio quite easily, yet the growth isn't linear;

x <- c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)
y <- c(53,55.2,57.4,59.8,62.3,64.9,67.5,70.3,73.2,76.2,79.3,82.5,85.9,89.3,92.8,96.4,100.2,104)

plot(x, y)

Giving this:

So I know ranging from 1 to 18 I have the values curving between 53 and 104, but what formula can give me say the 13th step's value?

Answer 1

I recommend entering your data in a new table in Desmos ...

https://www.desmos.com/calculator

then enter the following formula on the next line ...

$$y_1 \sim a x_1^2+bx_1+c$$

Desmos will return the best values of $a, b$ and $c$ to use in your formula.