Answer:
To write a piecewise function for the number of buses needed for a field trip according to the number of students attending, we need to consider the requirements stated in the question.
According to state law, one adult chaperone is required for every 10 students. Additionally, the maximum number of students that can go on a single field trip is 150.
Let's break down the different scenarios:
1. If the number of students is 0 or less than 0, no bus is needed.
2. If the number of students is between 1 and 150 (inclusive), we need to calculate the number of buses required based on the student count and the adult chaperone requirement.
- If the number of students is less than or equal to 10, only one bus is needed as the requirement can be fulfilled with a single chaperone.
- If the number of students is greater than 10, we need to calculate the number of buses required.
- Divide the number of students by 10 to determine the number of required chaperones.
- Round up the result to the nearest whole number to ensure that we have enough chaperones.
- Divide the rounded number by 48 (the maximum number of riders on a bus) to calculate the number of buses needed.
- Round up the result to the nearest whole number to ensure that we have enough buses.
3. If the number of students is greater than 150, the field trip cannot be accommodated due to the maximum capacity limit.
Based on these scenarios, we can write the piecewise function:
```
Number of Buses = {
0 if number of students ≤ 0
1 if 0 < number of students ≤ 10
ceil(number of students / 480) if 10 < number of students ≤ 150
undefined if number of students > 150
}
```
In this piecewise function, "ceil" represents the ceiling function, which rounds up to the nearest whole number.
Alli <3