Question

x | f(x)
1 | 48
2 | 36
3 | 27
4 | 20.25

make a function based off this table.
f(x) = ?

Answer 1

Notice each step multiplies by 36/48 = 27/36 = 20.25/27 = 3/4. This is a geometric sequence with first term 48 and ratio 3/4, so

f(x) = 48*(3/4)^{\,x-1}.

(Equivalently f(x)=64*(3/4)^x or f(x)=48*(0.75)^{x-1}.)