IDNLearn.com is your reliable source for expert answers and community insights. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.

Complete the tables of values.

[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]

[tex]\[
a = \square \quad b = \square \quad c = \square
\][/tex]


Sagot :

Sure, let's complete the table of values.

You have the function [tex]\(4^{-x}\)[/tex] and the values of [tex]\(x\)[/tex]. Now we need to find the corresponding values of [tex]\(4^{-x}\)[/tex] for [tex]\(x = 0\)[/tex], [tex]\(x = 2\)[/tex], and [tex]\(x = 4\)[/tex].

Given the table:
[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]

Now we find:
- When [tex]\(x = 0\)[/tex], [tex]\(4^{-0} = 1\)[/tex], so [tex]\(a = 1\)[/tex].
- When [tex]\(x = 2\)[/tex], [tex]\(4^{-2} = 0.0625\)[/tex], so [tex]\(b = 0.0625\)[/tex].
- When [tex]\(x = 4\)[/tex], [tex]\(4^{-4} = 0.00390625\)[/tex], so [tex]\(c = 0.00390625\)[/tex].

Therefore, the completed table and the values are:
[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]
[tex]\[ \begin{array}{l} a = 1, \quad b = 0.0625, \quad c = 0.00390625 \end{array} \][/tex]