Let's complete the given table step-by-step.
The original table is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $4^{- x }$ \\
\hline
-1 & 4 \\
\hline
0 & $a$ \\
\hline
2 & $b$ \\
\hline
4 & $c$ \\
\hline
\end{tabular}
\][/tex]
We need to determine the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
For [tex]\( x = 0 \)[/tex]:
[tex]\[ 4^{-0} = 1 \][/tex]
Thus, [tex]\( a = 1 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 4^{-2} = \frac{1}{16} \][/tex]
Thus, [tex]\( b = 0.0625 \)[/tex].
For [tex]\( x = 4 \)[/tex]:
[tex]\[ 4^{-4} = \frac{1}{256} \][/tex]
Thus, [tex]\( c = 0.00390625 \)[/tex].
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $4^{- x }$ \\
\hline
-1 & 4 \\
\hline
0 & 1 \\
\hline
2 & 0.0625 \\
\hline
4 & 0.00390625 \\
\hline
\end{tabular}
\][/tex]
Thus, we have:
[tex]\[ a = 1 \][/tex]
[tex]\[ b = 0.0625 \][/tex]
[tex]\[ c = 0.00390625 \][/tex]
