In a lab experiment, 30 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 7 hours. How many bacteria would there be after 16 hours, to the nearest whole number? Answer:

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Calculate Doublings: Determine the number of times the bacteria will double in 16 hours. Since the bacteria double every 7 hours, we divide the total time by the doubling period. 16 hours ÷ 7 hours per doubling period = 2.2857 doublings However, since bacteria can only double a whole number of times, we need to consider only complete doublings within the 16-hour period. 2 complete doublings will occur in 14 hours (2 × 7 hours).Calculate Bacteria After Doublings: Calculate the number of bacteria after the complete doublings. The initial number of bacteria is 30. After each doubling, the number of bacteria will multiply by 2. After 2 doublings: 30 × 2 × 2 = 30 × 4 = 120 bacteria.Remaining Time: Determine the remaining time after the last complete doubling. 16 hours - 14 hours = 2 hours remaining.Calculate Growth in 2 Hours: Calculate the growth of bacteria during the remaining 2 hours. Since the bacteria double every 7 hours, we need to find out how much they grow in 2 hours. Growth in 2 hours = 2 hours / 7 hours per doubling period. This is a fraction of a doubling period, so we need to raise 2 (the doubling factor) to the power of this fraction. Growth factor = 2^(2/7).Calculate Bacteria After 16 Hours: Calculate the number of bacteria after 16 hours. We multiply the number of bacteria after the complete doublings by the growth factor. Number of bacteria after 16 hours = 120 × 2^(2/7). Using a calculator, 2^(2/7) ≈ 1.24573. Number of bacteria after 16 hours ≈ 120 × 1.24573 ≈ 149.4876.Round to Nearest Whole Number: Round the number of bacteria to the nearest whole number. Since we cannot have a fraction of a bacterium, we round to the nearest whole number. Approximately 149.4876 rounds to 149 bacteria.

In a lab experiment, $30$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $7$ hours. How many bacteria would there be after $16$ hours, to the nearest whole number? $\newline$ Answer:

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In a lab experiment, $30$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $7$ hours. How many bacteria would there be after $16$ hours, to the nearest whole number? $\newline$ Answer: