Can you find a function that best models this relationship?

📌 CONCEPT: A function that models this relationship can be described as a linear function with variables representing the square of the number of students and the inverse of the number of trains.

📐 RULE / FORMULA: The function is given by f(x) = k × (n^2) / p, where 'n' is the number of students, 'p' is the number of trains, and 'k' is the constant of proportionality.

💡 WORKED EXAMPLE: If 10 buses were deployed when there were 400 students and 8 trains, we have f(400, 8) = 10. Substituting the values in the function, we get 10 = k × (400^2) / 8. Solving for 'k', we find k = 10 × 8 / (400^2) = 1.6 × 10^(-4). Therefore, the function is f(n, p) = 1.6 × 10^(-4) × (n^2) / p.

⚠️ COMMON MISTAKE: Students might confuse the direct and inverse proportionality, leading to incorrect formulation of the function.