Answer
a. $pH=6.0$
b. 6 min, $f(6)= 4.8$
c. $pH=6.5$
d. $pH=6.5$.
e. See explanations.
Work Step by Step
a. Based on the given graph, we can read the pH at 42 minutes to get $pH=6.0$
b. A minimum can be found at 6 min; using the equation, we have
$f(6)=\frac{6.5(6)^2-20.4(6)+234}{6^2+36}=4.8$
c. The normal pH level of the human mouth can be found to be $pH=6.5$, which happens at $t=0$ and $t\to\infty$
d. The horizontal asymptote can be found by letting $x\to\infty$ and we have $pH=6.5$. This means that without any more input of sugar or other food, the pH level should be close to 6.5 when waiting enough time.
e. Based on the graph, the pH value drops sharply at the beginning, reaching a minimum at 6 minutes and then it starts to rise slowly with time. The pH value reaches about 6.2 at the end of the first hour.
