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Answer :
Final answer:
To find the bacterial population after 80 minutes, we calculate 2.67 doubling times leading to approximately 19,200 bacteria. For 10 hours, with 20 doubling times, the population would be around 3,145,728,000 bacteria.
Explanation:
The student's question involves calculating the size of a bacterial population after a certain amount of time, given that it doubles every half hour. This is a classic example of exponential growth, which is often demonstrated by bacterial populations in ideal conditions.
Calculating Bacterial Population After 80 Minutes
Since the bacteria double every half hour (30 minutes), we first need to determine how many half-hour periods there are in 80 minutes. We divide 80 by 30, which gives us approximately 2.67 doubling times. Because the population doubles every half-hour, we use the formula N = N0 * 2t, where N0 is the initial population and t is the number of doubling times. Here, N0 is 3000 bacteria and t is 2.67. So the population after 80 minutes is about 3000 * 22.67, which we round to approximately 3,000 * 6.4, yielding 19,200 bacteria.
Calculating Bacterial Population After 10 Hours
Ten hours is equivalent to 20 half-hours (as 10 * 60 / 30 = 20), so there would be 20 doubling times. Using the same formula, we now have N = 3000 * 220. This calculates to 3000 multiplied by 1,048,576, resulting in a population of approximately 3,145,728,000 bacteria after 10 hours.
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