In a lab experiment, 6300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 8 hours. How many bacteria would there be after 19 hours, to the nearest whole number? Answer:

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Calculate Doubling Periods: Determine the number of times the bacteria population will double in 19 hours. Since the bacteria double every 8 hours, we divide the total time by the doubling period. 19 hours ÷ 8 hours per doubling period = 2.375 doubling periods.Calculate Bacteria After Doubling Periods: Since bacteria can only double a whole number of times, we need to consider only the whole number part of the doubling periods for the calculation. The number of complete doubling periods in 19 hours is 2 (since we cannot have a fraction of a doubling period).Calculate Remaining Time: Calculate the number of bacteria after the complete doubling periods. The population doubles 2 times, so we multiply the initial number of bacteria by 2 raised to the power of the number of doublings. 6300 bacteria × (2^2) = 6300 × 4 = 25200 bacteria after 16 hours (2 complete doubling periods).Calculate Growth During Remaining Time: Determine the remaining time after the last complete doubling period. 19 hours - 16 hours (2 complete doubling periods of 8 hours each) = 3 hours remaining.Apply Growth for Partial Period: Calculate the growth of bacteria during the remaining 3 hours. Since the bacteria double every 8 hours, we can find the fraction of doubling that occurs in 3 hours by dividing 3 by 8. 3 hours ÷ 8 hours per doubling period = 0.375 of a doubling period.Round Bacteria Count: Apply the growth for the partial doubling period to the bacteria count after 16 hours. We need to multiply the number of bacteria after 16 hours by 2 raised to the power of 0.375 to find the number of bacteria after the remaining 3 hours. 25200 bacteria × (2^0.375) ≈ 25200 × 1.333 ≈ 33600 bacteria after 19 hours.Round the result to the nearest whole number, as bacteria count cannot be a fraction. The number of bacteria after 19 hours, rounded to the nearest whole number, is approximately 33600.

In a lab experiment, $6300$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $8$ hours. How many bacteria would there be after $19$ hours, to the nearest whole number? $\newline$ Answer:

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In a lab experiment, $6300$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $8$ hours. How many bacteria would there be after $19$ hours, to the nearest whole number? $\newline$ Answer: