Answer
Both are exponential.
$f(x)=4.5\cdot 3^{x},\displaystyle \quad g(x)=2\cdot(\frac{1}{2})^{x}$
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 have
$\displaystyle \frac{1.5}{0.5}=3,\quad\frac{4.5}{1.5}=3,\quad\frac{13.5}{4.5}=3,\quad\frac{40.5}{13.5}=3$
so it is exponential, $f(x)=a\cdot 3^{x}.$
Since $f(0)=4.5$, so $a=4.5.$
Thus, $f(x)=4.5\cdot 3^{x}$
For the values of g(x),
$\displaystyle \frac{4}{8}=\frac{1}{2},\quad\frac{2}{4}=\frac{1}{2},\quad\frac{1}{2},\quad\frac{1/2}{1}=\frac{1}{2}$
so it is exponential, $g(x)=a\displaystyle \cdot(\frac{1}{2})^{x}.$
Since $g(0)=2$, so $a=2.$
Thus, $g(x)=2\displaystyle \cdot(\frac{1}{2})^{x},\qquad ($which can also be written as $2\cdot 2^{-x})$
