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The doubling period of a bacteria population is 27 minutes. after 48 minutes, the bacteria colony's population has grown to 13,332. determine the initial population of the bacteria colony. round the solution to the nearest whole number. determine the population of the bacteria colony after 2 hours. round the solution to the nearest whole number.

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Final answer:

The initial population of the bacteria colony is approximately 1326. The population of the bacteria colony after 2 hours is approximately 10981.

Step-by-step explanation:

To determine the initial population of the bacteria colony, we can use the concept of exponential growth. The doubling period of the bacteria population is 27 minutes, which means that the population doubles every 27 minutes. After 48 minutes, the population has grown to 13,332. To find the initial population, we can divide 13,332 by 2 raised to the power of 48 divided by 27.

Initial population = 13,332 / (2^(48/27)) ≈ 1326

So, the initial population of the bacteria colony is approximately 1326.

To determine the population of the bacteria colony after 2 hours, we need to find the number of doubling periods within 2 hours. Since the doubling period is 27 minutes, the number of doubling periods in 2 hours is 2 hours / 27 minutes. We can then multiply the initial population by 2 raised to the power of the number of doubling periods.

Number of doubling periods = 2 hours / 27 minutes = 4.44

Population after 2 hours = 1326 * (2^4.44) ≈ 10981

Therefore, the population of the bacteria colony after 2 hours is approximately 10981.

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