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In a lab experiment, 10 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 13 hours. How many bacteria would there be after 19 hours, to the nearest whole number? Answer:

In a lab experiment, 1010 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 1313 hours. How many bacteria would there be after 1919 hours, to the nearest whole number?\newlineAnswer:

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Q. In a lab experiment, 1010 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 1313 hours. How many bacteria would there be after 1919 hours, to the nearest whole number?\newlineAnswer:
  1. Understand Problem: Understand the problem and determine what is given and what needs to be found.\newlineWe know:\newlineInitial number of bacteria: 1010\newlineDoubling time: 1313 hours\newlineTotal time elapsed: 1919 hours\newlineWe need to find the number of bacteria after 1919 hours.
  2. Calculate Doubling Periods: Calculate the number of times the bacteria population will double in 1919 hours.\newlineTo find the number of doubling periods, we divide the total time by the doubling time.\newlineNumber of doubling periods =Total time elapsedDoubling time= \frac{\text{Total time elapsed}}{\text{Doubling time}}\newlineNumber of doubling periods =19 hours13 hours= \frac{19 \text{ hours}}{13 \text{ hours}}
  3. Find Bacteria After 11 Period: Perform the division to find the number of doubling periods.\newlineNumber of doubling periods = 19÷13≈1.4619 \div 13 \approx 1.46\newlineSince the number of bacteria can only double a whole number of times, we consider only the whole number part of the result, which is 11.
  4. Determine Final Bacteria Count: Calculate the number of bacteria after the whole number of doubling periods.\newlineAfter one doubling period, the number of bacteria will be:\newlineNumber of bacteria after 11 doubling period = Initial number of bacteria ×2Number of doubling periods\times 2^{\text{Number of doubling periods}}\newlineNumber of bacteria after 11 doubling period = 10×2110 \times 2^1\newlineNumber of bacteria after 11 doubling period = 10×210 \times 2\newlineNumber of bacteria after 11 doubling period = 2020
  5. Determine Final Bacteria Count: Calculate the number of bacteria after the whole number of doubling periods.\newlineAfter one doubling period, the number of bacteria will be:\newlineNumber of bacteria after 11 doubling period = Initial number of bacteria ×2Number of doubling periods\times 2^{\text{Number of doubling periods}}\newlineNumber of bacteria after 11 doubling period = 10×2110 \times 2^1\newlineNumber of bacteria after 11 doubling period = 10×210 \times 2\newlineNumber of bacteria after 11 doubling period = 2020Since the bacteria have not yet reached the second doubling period, we do not double the number again. The number of bacteria after 1919 hours will be approximately the same as after the first doubling period.\newlineFinal number of bacteria ≈\approx Number of bacteria after 11 doubling period\newlineFinal number of bacteria ≈20\approx 20

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