Answer
$
g(t)=1024 \cdot (0.5)^t
$
Work Step by Step
This table can represent an exponential function, since for every $\Delta t= 1$ , the value of $g(t)$ is have of the preceding value . This means that $b$ must be $\frac{1}{2}=0.5$. We can solve for $a$ by substituting in $(1,512)$
$$
\begin{aligned}
512 & =a \cdot 0.5^1 \\
512 & =a \cdot 0.5 \\
1024 & =a
\end{aligned}
$$ Hence, $$
g(t)=1024 \cdot (0.5)^t
$$
