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Select the correct answer from each drop-down menu.
[tex]\[ xy = -7159r + 3,00730 \][/tex]

\begin{tabular}{|c|c|}
\hline
7 & [tex]$y$[/tex] \\
\hline
0 & \[tex]$8,000 \\
\hline
1 & 57,888 \\
\hline
2 & 57,775 \\
\hline
3 & 57,661 \\
\hline
4 & 57,547 \\
\hline
5 & 57,432 \\
\hline
6 & \$[/tex]7,316 \\
\hline
7 & 57,200 \\
\hline
8 & 57,083 \\
\hline
9 & \[tex]$6,966 \\
\hline
10 & 56,843 \\
\hline
11 & 56,729 \\
\hline
12 & 56,609 \\
\hline
\end{tabular}

According to the line of best fit and using $[/tex]\square[tex]$, Sean can estimate that the balance of his loan will reach 50 in month $[/tex]\square[tex]$ to $[/tex]\square[tex]$.

- Interpolation
- Extrapolation

$[/tex]\square=1$



Answer :

GinnyAnswer
To answer the given question, let’s break it down step-by-step:

1. Understanding the Data:
- You have a table of monthly data points where [tex]\( x \)[/tex] represents the month and [tex]\( y \)[/tex] represents the balance.
- The data points range from [tex]\( x = 0 \)[/tex] to [tex]\( x = 12 \)[/tex].

2. Line of Best Fit:
- For predicting values, we often use a line of best fit (or trend line), which is a straight line that best approximates the data.
- However, the exact nature of this hypothetical best fit line isn't given in the specific terms you might expect in such problems (like a particular linear equation), but we can infer that from the provided data trend or earlier given information that implies a decrement pattern.

3. Reaching a Specific Balance:
- We need to calculate when the balance [tex]\( y \)[/tex] will reach 50. Looking at the data trends, the balance never goes anywhere near that low on the given time scale.
- Realistically, based on the balance trend, we need to predict this value way outside the currently given range through extrapolation.

4. Definition: Interpolation vs. Extrapolation:
- Interpolation: It is used to estimate values within the range of the data points.
- Extrapolation: It is used to estimate values outside the range of the data points.

5. Choosing:
- Since 50 is a value well outside the range of provided data, we need to use extrapolation.

Hence, the true answer is:

Extrapolation

Given our understanding, we can't predict the exact month accurately because it requires actual calculation from the data trend or formula, which is implied here rather than stated mathematically.

So, the balance of his loan reaching 50 USD falls outside the given data points and requires extrapolation.

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