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 14 hours. How many bacteria would there be after 4 hours, to the nearest whole number? Answer:

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Understand the problem: Understand the problem and determine what is being asked. We need to calculate the number of bacteria after 4 hours, knowing that the initial count is 30 and they double every 14 hours. Since 4 hours is not a full doubling period, we need to find out how much growth occurs in 4 hours as a fraction of the 14-hour doubling period.Calculate fraction of period: Calculate the fraction of the doubling period that has passed after 4 hours. 4 hours is 4/14 of the 14-hour period. Fraction of the doubling period = 4/14Convert fraction to growth factor: Convert the fraction of the doubling period into a growth factor. Since the bacteria double every full period, we need to find the growth factor for the fraction of the period. This can be done using the formula for exponential growth: N = N0 * 2^(t/T), where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the doubling time. Growth factor for 4 hours = 2^(4/14)Calculate growth factor: Calculate the growth factor using the fraction obtained in Step 2. Growth factor for 4 hours = 2^(4/14) ≈ 2^(0.2857) Using a calculator, we find that 2^(0.2857) ≈ 1.3348Apply growth factor: Apply the growth factor to the initial number of bacteria to find the number after 4 hours. Number of bacteria after 4 hours = Initial number of bacteria * Growth factor Number of bacteria after 4 hours ≈ 30 * 1.3348Perform multiplication: Perform the multiplication to find the number of bacteria after 4 hours. Number of bacteria after 4 hours ≈ 30 * 1.3348 ≈ 40.044Round the result: Round the result to the nearest whole number, as the question asks for an approximation. Number of bacteria after 4 hours, rounded = 40 (to the nearest whole number)

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 $14$ hours. How many bacteria would there be after $4$ 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 $14$ hours. How many bacteria would there be after $4$ hours, to the nearest whole number? $\newline$ Answer: