To determine the tunnel length 26 days after the TBM was introduced, we can use a method called linear interpolation. The data provided shows the length of the tunnel at specific days, and we can estimate the tunnel length at a day that falls between two of these specific days.
Let's use the table data to find two points (days and corresponding tunnel lengths) that sandwich day 26:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Days} & \text{Tunnel Length (feet)} \\
\hline
20 & 1040 \\
\hline
28 & 1400 \\
\hline
\end{array}
\][/tex]
Now let's apply linear interpolation between these two points. The formula for linear interpolation between two points [tex]\((x_0, y_0)\)[/tex] and [tex]\((x_1, y_1)\)[/tex] to find [tex]\(y\)[/tex] at a given [tex]\(x\)[/tex] is:
[tex]\[
y = y_0 + (y_1 - y_0) \times \frac{(x - x_0)}{(x_1 - x_0)}
\][/tex]
Here:
- [tex]\((x_0, y_0) = (20, 1040)\)[/tex]
- [tex]\((x_1, y_1) = (28, 1400)\)[/tex]
- [tex]\(x = 26\)[/tex]
Substitute these values into the formula to find [tex]\(y\)[/tex]:
[tex]\[
y = 1040 + (1400 - 1040) \times \frac{(26 - 20)}{(28 - 20)}
\][/tex]
First, calculate the difference in [tex]\(y\)[/tex] values:
[tex]\[
1400 - 1040 = 360
\][/tex]
Next, calculate the fraction:
[tex]\[
\frac{(26 - 20)}{(28 - 20)} = \frac{6}{8} = \frac{3}{4}
\][/tex]
Multiply the difference by this fraction:
[tex]\[
360 \times \frac{3}{4} = 360 \times 0.75 = 270
\][/tex]
Now add this result to the initial [tex]\(y\)[/tex] value:
[tex]\[
y = 1040 + 270 = 1310
\][/tex]
Therefore, the tunnel length 26 days after the TBM was introduced is:
[tex]\[
\boxed{1310 \text{ feet}}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\text{B. 1,310 feet}
\][/tex]
