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A biology class at Central High School predicted that a local population of animals will double in size every $12$ years. The population at the beginning of $2014$ was estimated to be $50$ animals. If $P$ represents the population $n$ years after $2014$, then which of the following equations represents the class’s model of the population over time?$\newline$A) $P = 12 + 50n$$\newline$B) $P = 50 + 12n$$\newline$C) $P = 50(2)^{12n}$$\newline$D) $P = 50(2)^{\frac{n}{12}}$