Answer
Neither is exponential.
Work Step by Step
If a function x is an exponential function, then it has form
$f(x)=a\cdot b^{x}$
When we observe an increase of x by 1 unit, $f(x+1)=ab^{x+1}.$
what follows is that the ratio $\displaystyle \frac{f(x+1)}{f(x)}=\frac{ab^{x+1}}{ab^{x}}=b.$
(the ratio is constant when arguments increase by 1).
Thus, if the x increases by unit, the function value is multiplied with b.
We use this to recognize whether a table of function values represent an exponential function or not.
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The x-values increase by 1 unit.
For the values of f(x) we observe $ \displaystyle \frac{f(x+1)}{f(x)}$:
$\displaystyle \frac{0.2}{0.8}=\frac{1}{4},\quad \displaystyle \frac{0.1}{0.2}\neq\frac{1}{4}\quad $
so f is not exponential.
For the values of g(x)
$\displaystyle \frac{40}{80}=\frac{1}{2},\quad \displaystyle \frac{20}{40}=\frac{1}{2},\quad \displaystyle \frac{10}{20}=\frac{1}{2},\quad \displaystyle \frac{2}{10}\neq\frac{1}{2},\quad$
so g is not exponential.
Neither is exponential.
