astronomers classify stars

Question

astronomers classify stars according to their brightness by assigning them a stellar magnitude. the higher the magnitude the dimmer the star. the dimmest stars visible to the naked eye have stellar magnitudes of 6.. the table below shows the relative brightness of different stellar magnitudes. stellar magnitude

1 2 3 4 5 6

relative brightness 100 40 16 6.3 2.5 1

a.find an equation

that gives the relative brightness in terms of stellar magnitude.

b. use this equation to find the relative brightness of a star with magnitude 9.

i got parts of it right

Answer 1

The sequence 100, 40, 16, 6.3, 2.5, 1 is approximately geometric with common ratio r = 0.4.

If x = stellar magnitude, then f(x) = 100(0.4)^x-1 = relative brightness

So, f(9) = 100(0.4)⁸ ≈ 0.066

Answer 2

I figure x/10+4 is your formula.