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The population of City Z was $50$,$000$ in $1983$ . From $1983$ to $2013$, the population of City Z doubled every $5$ years. Which of the following best models $P$, the population of City Z from $1983$ to $2013, t$ years after $1983$ ?$\newline$Choose $1$ answer:$\newline$(A) $P=50,000(2)^{\frac{t}{5}}$$\newline$(B) $P=50,000(2)^{\mathrm{Br}}$$\newline$(C) $P=10,000 t+50,000$$\newline$(D) $P=20,000 t+50,000$