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Which of the following best describes how the [tex]$y$[/tex] values are changing over each interval?

\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & 2 \\
\hline 2 & 4 \\
\hline 3 & 8 \\
\hline 4 & 16 \\
\hline 5 & 32 \\
\hline
\end{tabular}

A. They are increasing by 2 each time.

B. They are being multiplied by 2 each time.

Sagot :

GinnyAnswer
To determine how the \( y \) values are changing over each interval given in the table, let's analyze the pattern:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 2 \\ \hline 2 & 4 \\ \hline 3 & 8 \\ \hline 4 & 16 \\ \hline 5 & 32 \\ \hline \end{array} \][/tex]

1. From \( x = 1 \) to \( x = 2 \):

[tex]\[ \frac{y_{\text{at } x=2}}{y_{\text{at } x=1}} = \frac{4}{2} = 2 \][/tex]

The \( y \) value is multiplied by 2.

2. From \( x = 2 \) to \( x = 3 \):

[tex]\[ \frac{y_{\text{at } x=3}}{y_{\text{at } x=2}} = \frac{8}{4} = 2 \][/tex]

The \( y \) value is multiplied by 2.

3. From \( x = 3 \) to \( x = 4 \):

[tex]\[ \frac{y_{\text{at } x=4}}{y_{\text{at } x=3}} = \frac{16}{8} = 2 \][/tex]

The \( y \) value is multiplied by 2.

4. From \( x = 4 \) to \( x = 5 \):

[tex]\[ \frac{y_{\text{at } x=5}}{y_{\text{at } x=4}} = \frac{32}{16} = 2 \][/tex]

The \( y \) value is multiplied by 2.

In conclusion, the \( y \) values in the table are changing by being multiplied by 2 each time. Therefore, the correct description of how the \( y \) values are changing over each interval is:

They are being multiplied by 2 each time.
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