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The population of bacteria in a colony becomes 10 times its original amount at the end of n days. After how many hours will the population become 100 times its original amount?

Answer :

Final answer:

The bacterial population grows exponentially, with each bacteria dividing about every hour. To calculate the time needed for the bacterial population to become 100 times larger, you need to solve the equation 2^n = 100 for n, which gives approximately 6.64. Thus, it will take about 6.64 hours.

Explanation:

The bacterial population grows exponentially, which means its growth rate increases over time due to each organism continuously dividing and reproducing. This type of growth is often seen in bacteria. In many bacterial species, division takes roughly an hour. Therefore, if you start with a single bacterium, it will divide to become two bacteria after one hour, then these two bacteria will divide to become four bacteria after the second hour, eight bacteria after the third hour, and so on. This is an example of exponential growth.

If you want the population to become 100 times larger, this means you need enough division cycles whereby the number of bacteria doubles each time to reach 100 times the original number. In mathematical terms, if we represent the number of cycles as 'n', we need to solve the equation 2^n = 100. Using a logarithm calculator, n is approximately 6.64.

Remember that one division cycle takes roughly an hour for many bacteria, thus, approximately 6.64 hours are needed for the bacterial population to become 100 times its original size. Please note that this is a simplified example and in the real world the growth rate of bacteria can be influenced by many factors such as availability of nutrients, temperature, and presence of other organisms.

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