To determine the explicit formula for the sequence of the number of bacteria, we need to analyze the options provided and determine which one correctly represents the growth pattern of the bacteria based on the data in the table.
Let's break down the responses:
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an = n + 21: This suggests a linear growth where the number of bacteria increases by 1 for each hour, starting at 21.
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an = 121n: This indicates that the number of bacteria is directly proportional to n, scaled by 121.
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an = 21n: This option suggests that the number of bacteria increases linearly with n, where the growth rate is 21.
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an = 21n + 21: Here, the bacteria grow linearly with n, but with an initial offset of 21.
Without the specific growth data, it's difficult to select the exact correct formula. However, based on common bacterial growth patterns, it could be exponential rather than strictly linear.
Assuming that "an" indicates the number of bacteria at hour n, and based on common models, if you see consistent doubling or tripling in numbers, it could hint at an exponential function.
However, if you're strictly choosing among your given options and assuming linear growth is the pattern you see, the best choices can be:
If initial bacteria start at 21 and grow by a constant rate:
- If the growth appears constant, an = 21n + 21 could suggest bacteria starts at 21 and increases consistently.
So without the table data, it's tricky, but based on possible interpretations, I can suggest you consider an = 21n + 21.
Please choose the option that best fits the pattern you see in your data.