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Frank catches a cold. The next day he goes to school and $3$ of his classmates catch a cold. Each day thereafter, the number of people catching a cold triples. Let $C$ be the number of people who catch a cold on day $t$. Which of the following best explains the relationship between $t$ and $C$ ?$\newline$Choose $1$ answer:$\newline$(A) The relationship is exponential because $C$ increases by $6$ as $t$ increases from $t=1$ to $t=2$.$\newline$(B) The relationship is linear because $C$ increases by a factor of $3$ each time $t$ increases by $1$ .$\newline$(C) The relationship is exponential because $C$ increases by a factor of $3$ each time $t$ increases by $1$ .$\newline$(D) The relationship is linear because $C$ increases by $2$ as $t$ increases from $t=0$ to $t=1$.