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A population grows according to P(t)=200⋅2t3P(t)=200\(\cdot\)2^{\(\frac{t}{3}\)}, where tt is in months. Solve for tt when P(t)=1600P(t) = 1600.

A population grows according to $P (t) = 200 \cdot 2^{\frac{t}{3}}$ , where $t$ is in months. Solve for $t$ when $P of t equals 1600$ .