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Is the number of students on a field trip a function of the number of buses used? Explain.Question
Is the number of students on a field trip a function of the number of buses used. Explain
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GPT-4o mini
To determine whether the number of students on a field trip is a function of the number of buses used, we need to consider the definition of a function.
A function is a relation in which each input (in this case, the number of buses) corresponds to exactly one output (the number of students). In other words, for each number of buses used, there should be a unique number of students that can be transported.
If we assume that each bus can carry a fixed number of students (let's say \( S \) students per bus), then the total number of students \( N \) can be calculated as:
\[
N = B \times S
\]
where \( B \) is the number of buses. In this context:
- If \( B = 1 \), then \( N = S \).
- If \( B = 2 \), then \( N = 2S \).
- If \( B = 3 \), then \( N = 3S \).
As long as each bus has the same capacity, for any given number of buses \( B \), there is exactly one corresponding number of students \( N \).
However, if we introduce variables such as varying bus capacities, or if some buses are left empty, then the relationship might not hold true as a function anymore. For example, if one of the buses holds fewer students or if not all buses are filled, the relationship could become uncertain.
In conclusion, under the assumption that each bus transports a consistent and fixed number of students, the number of students on a field trip is indeed a function of the number of buses used.
A function is a relation in which each input (in this case, the number of buses) corresponds to exactly one output (the number of students). In other words, for each number of buses used, there should be a unique number of students that can be transported.
If we assume that each bus can carry a fixed number of students (let's say \( S \) students per bus), then the total number of students \( N \) can be calculated as:
\[
N = B \times S
\]
where \( B \) is the number of buses. In this context:
- If \( B = 1 \), then \( N = S \).
- If \( B = 2 \), then \( N = 2S \).
- If \( B = 3 \), then \( N = 3S \).
As long as each bus has the same capacity, for any given number of buses \( B \), there is exactly one corresponding number of students \( N \).
However, if we introduce variables such as varying bus capacities, or if some buses are left empty, then the relationship might not hold true as a function anymore. For example, if one of the buses holds fewer students or if not all buses are filled, the relationship could become uncertain.
In conclusion, under the assumption that each bus transports a consistent and fixed number of students, the number of students on a field trip is indeed a function of the number of buses used.