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```plaintext
| x | y |
|--------|------|
| 1 | 2 |
| 10 | a |
| 100 | b |
| 10,000 | c |
|100,000 | d |
|1,000,000 | e |
```

Sagot :

GinnyAnswer
To determine the values for [tex]\(y\)[/tex] corresponding to the given [tex]\(x\)[/tex] values, we need to establish a relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. Let's start by analyzing the information we have.

Given values:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & 2 \\ \hline 10 & $a$ \\ \hline 100 & $b$ \\ \hline 10,000 & $c$ \\ \hline 100,000 & $d$ \\ \hline 1,000,000 & $e$ \\ \hline \end{tabular} \][/tex]

From the table, when [tex]\(x = 1\)[/tex], we have [tex]\( y = 2 \)[/tex]. This suggests [tex]\( y \)[/tex] might be a function of [tex]\( x \)[/tex]. A common and simple relationship we can try is a power or an exponential relationship.

Let's assume [tex]\( y \)[/tex] is related to [tex]\( x \)[/tex] by a simple power relationship of the form:
[tex]\[ y = k \cdot x^n \][/tex]

Given [tex]\( x = 1 \)[/tex], [tex]\( y = 2 \)[/tex]:
[tex]\[ 2 = k \cdot 1^n \][/tex]
[tex]\[ k = 2 \][/tex]

So our equation becomes:
[tex]\[ y = 2 \cdot x^n \][/tex]

Next, we need to find the value of [tex]\( n \)[/tex]. We do not have direct information to determine [tex]\( n \)[/tex] from the other values, but we need to assume it to proceed further. Let's assume [tex]\( n = 1 \)[/tex] as it is a simple and commonly seen linear relationship.

Using [tex]\( n = 1 \)[/tex]:
[tex]\[ y = 2 \cdot x \][/tex]

Now let's calculate the values:

1. For [tex]\( x = 10 \)[/tex]:
[tex]\[ y = 2 \cdot 10 = 20 \][/tex]
Thus, [tex]\( a = 20 \)[/tex].

2. For [tex]\( x = 100 \)[/tex]:
[tex]\[ y = 2 \cdot 100 = 200 \][/tex]
Thus, [tex]\( b = 200 \)[/tex].

3. For [tex]\( x = 10,000 \)[/tex]:
[tex]\[ y = 2 \cdot 10,000 = 20,000 \][/tex]
Thus, [tex]\( c = 20,000 \)[/tex].

4. For [tex]\( x = 100,000 \)[/tex]:
[tex]\[ y = 2 \cdot 100,000 = 200,000 \][/tex]
Thus, [tex]\( d = 200,000 \)[/tex].

5. For [tex]\( x = 1,000,000 \)[/tex]:
[tex]\[ y = 2 \cdot 1,000,000 = 2,000,000 \][/tex]
Thus, [tex]\( e = 2,000,000 \)[/tex].

Summarizing, the completed table is:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & 2 \\ \hline 10 & 20 \\ \hline 100 & 200 \\ \hline 10,000 & 20,000 \\ \hline 100,000 & 200,000 \\ \hline 1,000,000 & 2,000,000 \\ \hline \end{tabular} \][/tex]
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