To determine the temperature of the water as time approaches 60 minutes, we need to observe the trend in the given temperature data. Let's analyze the data available:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Time } ( \text{min} ) & 0 & 10 & 20 & 30 & 40 & 50 \\
\hline
\text{Temp } (\text{°F}) & 32 & 40 & 60 & 68 & 68 & 68 \\
\hline
\end{array}
\][/tex]
We notice that as time increases, the temperature of the water initially rises and then stabilizes. Beyond 30 minutes, the temperature remains constant at 68°F.
To express this mathematically, we use the concept of limits. The notation for the limit of the temperature function [tex]\( f(x) \)[/tex] as [tex]\( x \)[/tex] (time) approaches 60 minutes is given by:
[tex]\[
\lim_{{x \to 60}} f(x)
\][/tex]
From the data, we observe that the temperature [tex]\( f(x) \)[/tex] stabilizes at 68°F. Therefore, we can write:
[tex]\[
\lim_{{x \to 60}} f(x) = 68
\][/tex]
This means that as time approaches 60 minutes, the temperature of the water approaches 68°F and remains constant at that value.
