The Following Table Gives $A(t)$ , the Percentage of the Electorate Favoring Candidate

Multiple Choice

The following table gives $A(t)$ , the percentage of the electorate favoring candidate $A$ during the 12 months preceding a presidential election. Time, $t$ , is measured in months, and $t=0$ is a year before election day.

Assume that $A(t)$ is approximately trigonometric. A second candidate, candidate $B$ , has a percentage of candidate support given by $B(t) =31+15 \sin \left(\frac{\pi}{6} t\right)$ . Let $f(t) =A(t) +B(t)$ for $0 \leq t \leq 12$ . What is the meaning of the minimum of $f(t)$ ?

A) The minimum percentage lead candidate $A$ has over candidate $B$ .
B) The minimum percentage lead candidate $B$ has over candidate $A$ .
C) The minimum combined percentage of the electorate favoring either candidate $A$ or candidate $B$ .
D) The minimum combined percentage of the electorate favoring neither candidate $A$ nor candidate $B$ .