In a lab experiment, 70 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 15 hours. How many bacteria would there be after 29 hours, to the nearest whole number? Answer:

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Determine Doubling Periods: First, we need to determine how many times the bacteria population can double in 29 hours. Since the bacteria double every 15 hours, we divide the total time by the doubling period. 29 hours ÷ 15 hours per doubling period = 1.9333 doubling periods.Calculate Full Periods: Since the bacteria can only double an integer number of times, we need to consider how many full doubling periods occur within 29 hours. We can't have a fraction of a doubling period, so we take the floor of the previous result. Full doubling periods = 1 (since 1.9333 indicates that only one full doubling period has occurred within 29 hours).Calculate After 1 Period: Now we calculate the number of bacteria after one full doubling period. We start with 70 bacteria and double it once. Number of bacteria after 1 doubling period = 70 × 2^1 = 70 × 2 = 140 bacteria.Estimate Growth: We have 14 hours remaining after the first doubling period (29 hours - 15 hours = 14 hours). We need to estimate the growth during this period. Since the bacteria double every 15 hours, we can use the fraction of the doubling period that has passed (14/15) to estimate the growth. Fraction of doubling period passed = 14/15.Calculate Growth Factor: We calculate the growth factor for the remaining 14 hours using the fraction of the doubling period. Growth factor for 14 hours = 2^(14/15).Apply Growth Factor: Now we apply the growth factor to the number of bacteria after the first doubling period to estimate the total number of bacteria after 29 hours. Estimated number of bacteria after 29 hours = 140 × 2^(14/15).Calculate Estimated Bacteria: We perform the calculation for the growth factor and then multiply by the number of bacteria after the first doubling period. 2^(14/15) ≈ 1.897 (rounded to three decimal places for simplicity). Estimated number of bacteria after 29 hours ≈ 140 × 1.897.Round to Nearest Whole: Finally, we calculate the estimated number of bacteria to the nearest whole number. Estimated number of bacteria after 29 hours ≈ 140 × 1.897 ≈ 265.58. Since we need to report the number of bacteria to the nearest whole number, we round 265.58 to 266.

In a lab experiment, $70$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $15$ hours. How many bacteria would there be after $29$ hours, to the nearest whole number? $\newline$ Answer:

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In a lab experiment, 707070 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 151515 hours. How many bacteria would there be after 292929 hours, to the nearest whole number?\newlineAnswer:

In a lab experiment, $70$ bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every $15$ hours. How many bacteria would there be after $29$ hours, to the nearest whole number? $\newline$ Answer: