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Complete the table of values.

| x | [tex]\( 4^{-x} \)[/tex] |
|----|------------|
| -1 | 4 |
| 0 | [tex]\( a \)[/tex] |
| 2 | [tex]\( b \)[/tex] |
| 4 | [tex]\( c \)[/tex] |

[tex]\( a = \square \)[/tex]
[tex]\( b = \square \)[/tex]
[tex]\( c = \square \)[/tex]

Sagot :

GinnyAnsweridn
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]
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