Answer
The pH tends to $6.5$ as $x\rightarrow \infty$
Work Step by Step
We are given the function:
$$f(x)=\dfrac{6.5x^2-20.4x+234}{x^2+36}.\tag1$$
Graph the function $f$.
We notice that for $x>42$ the pH level $x$ minutes after a person eats food containing sugar is between $6$ and $6.5$. The more time passes, the closer to the value $6.5$ the pH gets. In fact the graph has a horizontal asymptote $y=6.5$, so the value of pH is close to $6.5$ as $x$ increases indefinitely.
