A group of students wishes to charter a bus for an educational tour that can accommodate at most 50 students. The bus company requires at least 35 students for that trip. The bus company charges Rs. 200 per student up to the strength of 45.

For more than 45 students, the company charges each student Rs. 200 less 1/5 times more than 45. Consider the number of students participating in the tour as a function, and find the total cost and domain.plot graph

Here's the graph representing the total cost \( C(n) \) as a function of the number of students \( n \) for the educational tour.

### Summary:
- **Domain**: \( 35 \leq n \leq 50 \)
- **Cost Function**:
  - For \( 35 \leq n \leq 45 \), the total cost is \( C(n) = 200n \).
  - For \( 46 \leq n \leq 50 \), the total cost is \( C(n) = 209n - \frac{n^2}{5} \).

The graph shows a linear increase in cost for \( n \) from 35 to 45 and a slightly curved path for \( n \) from 46 to 50, reflecting the discount applied per student.

Would you like more details on this or have any other questions?

Here are 5 related questions:
1. What happens to the cost function if the company changes the price per student to Rs. 250?
2. How would the function change if the discount formula for more than 45 students was altered?
3. What would be the impact on the total cost if the number of students is less than 35?
4. Can the maximum number of students affect the overall total cost trend?
5. How can we determine the exact number of students that will minimize the cost per student?

**Tip:** Understanding how a piecewise function works can help in modeling real-life situations where rules or conditions change based on certain thresholds.

Explore the total cost function analysis for an educational tour involving bus chartering. Learn about the piecewise function structure and quadratic formula application. Suitable for high school students studying functions and quadratic equations.

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