Table 1.2 shows the average annual sea level, S, in meters,...

Table 1.2 shows the average annual sea level, $S$, in meters, in Aberdeen, Scotland, $^{10}$ as a function of time, $t$ measured in years before 2008. Table 1.2 $$\begin{array}{|c|c|c|c|c|c|c|}\hline t & 0 & 25 & 50 & 75 & 100 & 125 \\\hline S & 7.094 & 7.019 & 6.992 & 6.965 & 6.938 & 6.957 \\\hline\end{array}$$ (a) What was the average sea level in Aberdeen in $2008 ?$ (b) In what year was the average sea level 7.019 meters? 6.957 meters? (c) Table 1.3 gives the average sea level, $S$, in Aberdeen as a function of the year, $x$. Complete the missing values. Table 1.3 $$\begin{array}{|c|c|c|c|c|c|c|}\hline x & 1883 & ? & 1933 & 1958 & 1983 & 2008 \\\hline S & ? & 6.938 & ? & 6.992 & ? & ? \\\hline\end{array}$$

Table 1.2 shows the average annual sea level, $S$, in meters, in Aberdeen, Scotland, $^{10}$ as a function of time, $t$ measured in years before 2008.
Table 1.2
$$\begin{array}{|c|c|c|c|c|c|c|}\hline t & 0 & 25 & 50 & 75 & 100 & 125 \\\hline S & 7.094 & 7.019 & 6.992 & 6.965 & 6.938 & 6.957 \\\hline\end{array}$$
(a) What was the average sea level in Aberdeen in $2008 ?$
(b) In what year was the average sea level 7.019 meters? 6.957 meters?
(c) Table 1.3 gives the average sea level, $S$, in Aberdeen as a function of the year, $x$. Complete the missing values.
Table 1.3
$$\begin{array}{|c|c|c|c|c|c|c|}\hline x & 1883 & ? & 1933 & 1958 & 1983 & 2008 \\\hline S & ? & 6.938 & ? & 6.992 & ? & ? \\\hline\end{array}$$

Key Concepts

Interpreting Tabular Data

This concept involves reading and understanding data presented in tables. It includes identifying the variables (in this case, time and sea level) and extracting their corresponding values, which is fundamental for analyzing relationships and trends within the dataset.

Time Variable Transformation

This concept refers to converting between different ways of representing time. In the problem, time is given relative to a base year (2008) in one table and as actual calendar years in another. Recognizing and applying the correct transformation between these representations is crucial for accurate analysis.

Linear Interpolation

Linear interpolation is a method used to estimate values within two known data points in a table. When values for certain time intervals are missing, this technique assumes a straight-line change between known points to approximate the missing values.

Inverse Function Application

This concept involves determining the input value that corresponds to a given output value. In the context of the problem, it means finding the time or year at which a specific sea level is reached by effectively 'reversing' the function defined by the table data.

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