High School

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A culture of bacteria has an initial population of 230 bacteria and doubles every 9 hours. Using the formula

\[
P_t = P_0 \cdot 2^{\frac{t}{d}}
\]

where \( P_t \) is the population after \( t \) hours, \( P_0 \) is the initial population, \( t \) is the time in hours, and \( d \) is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?