What is the formula that would calculate this graph?

Question

y = brightness in percentage
x = apparent magnitude

What is a formula that would result in the graph below, with y representing the brightness in percentage and x the apparent magnitude (also accounting for negative values)?

To clarify: Each decrease by 1 in apparent magnitude will require the star to have only 100/fifth root of 100 of the illumination as it used to be

Answer 1

The definition of magnitude in astronomy is that an increase of $1$ in magnitude is a factor $2.5$ reduction in brightness. So if $m$ is the magnitude, we have $$y=100\cdot 2.5^{1-x}$$

Answer 2

The function

$$y = -22 + 122/x$$

works fine.

Answer 3

$$B(M)= 250(0.4)^{M} $$

obtained by fitting $y=kb^x$ using the points $(1,100)$ and $(2,40)$