I can eyeball points (1/2, 8), (1,4), (2,1), (3,1/4)
The pattern is each increment of 1/2 in x divides by two.

Any of the points give k=16

Check: x=1/2 4^(3/2)=2^2=8 good
x=1 4^(2-1)=4 good
x=2 4^(2-2)=1 good
x=3 4^(2-3)=1/4 good
I believe that the common difference would be.10
Suggestion:
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