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

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

A. They are increasing by 2 each time.
B. They are increasing by 4 each time.
C. They are being multiplied by 2 each time.
D. They are being multiplied by 4 each time.

Sagot :

GinnyAnsweridn
Let's analyze how the [tex]\( y \)[/tex] values change as the [tex]\( x \)[/tex] values increase.

Given the data:
[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]

We can calculate the changes in the [tex]\( y \)[/tex] values for each interval:
- From [tex]\( x = 1 \)[/tex] to [tex]\( x = 2 \)[/tex], the [tex]\( y \)[/tex] value changes from 2 to 4.
- From [tex]\( x = 2 \)[/tex] to [tex]\( x = 3 \)[/tex], the [tex]\( y \)[/tex] value changes from 4 to 8.
- From [tex]\( x = 3 \)[/tex] to [tex]\( x = 4 \)[/tex], the [tex]\( y \)[/tex] value changes from 8 to 16.
- From [tex]\( x = 4 \)[/tex] to [tex]\( x = 5 \)[/tex], the [tex]\( y \)[/tex] value changes from 16 to 32.

Next, let's observe the pattern of change in [tex]\( y \)[/tex]:

1. [tex]\( 4 / 2 = 2 \)[/tex]
2. [tex]\( 8 / 4 = 2 \)[/tex]
3. [tex]\( 16 / 8 = 2 \)[/tex]
4. [tex]\( 32 / 16 = 2 \)[/tex]

In each interval, the [tex]\( y \)[/tex] value is being multiplied by 2. This indicates that the [tex]\( y \)[/tex] values are consistently multiplied by 2 as the [tex]\( x \)[/tex] values increase by 1.

Thus, the best description of how the [tex]\( y \)[/tex] values are changing over each interval is:
[tex]\[ \boxed{\text{They are being multiplied by 2 each time.}} \][/tex]
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